Oblique derivative problems for elliptic equations:
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| Format: | Elektronisch E-Book |
| Sprache: | English |
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World Scientific
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| Beschreibung: | Includes bibliographical references and index 1. Pointwise estimates. 1.1. The maximum principle. 1.2. The definition of obliqueness. 1.3. The case c < 0, [symbol]. 1.4. A generalized change of variables formula. 1.5. The Aleksandrov-Bakel'man-Pucci maximum principles. 1.6. The interior weak Harnack inequality. 1.7. The weak Harnack inequality at the boundary. 1.8. The strong maximum principle and uniqueness. 1.9. Hölder continuity. 1.10. The local maximum principle. 1.11. Pointwise estimates for solutions of mixed boundary value problems. 1.12. Derivative bounds for solutions of elliptic equations -- 2. Classical Schauder theory from a modern perspective. 2.1. Definitions and properties of Hölder spaces. 2.2. An alternative characterization of Hölder spaces. 2.3. An existence result. 2.4. Basic interior estimates. 2.5. The Perron process for the Dirichlet problem. 2.6. A model mixed boundary value problem. 2.7. Domains with curved boundary. 2.8. Fredholm-Riesz-Schauder theory -- - 3. The Miller barrier and some supersolutions for oblique derivative problems. 3.1. Theory of ordinary differential equations. 3.2. The Miller barrier construction. 3.3. Construction of supersolutions for Dirichlet data. 3.4. Construction of a supersolution for oblique derivative problems. 3.5. The strong maximum principle, revisited. 3.6. A Miller barrier for mixed boundary value problems -- 4. Hölder estimates for first and second derivatives. 4.1. C[symbol] estimates for continuous [symbol]. 4.2. Regularized distance. 4.3. Existence of solutions for continuous [symbol]. 4.4. Hölder gradient estimates for the Dirichlet problem. 4.5. C[symbol] estimates with discontinuous [symbol] in two dimensions. 4.6. C[symbol] estimates for discontinuous [symbol] in higher dimensions. 4.7. C[symbol] estimates -- - 5. Weak solutions. 5.1. Definitions and basic properties of weak derivatives. 5.2. Sobolev imbedding theorems. 5.3. Poincaré's inequality. 5.4. The weak maximum principle. 5.5. Trace theorems. 5.6. Existence of weak solutions. 5.7. Higher regularity of solutions. 5.8. Global boundedness of weak solutions. 5.9. The local maximum principle. 5.10. The DeGiorgi class. 5.11. Membership of supersolutions in the De Giorgi class. 5.12. Consequences of the local estimates. 5.13. Integral characterizations of Hölder spaces. 5.14. Schauder estimates -- - 6. Strong solutions. 6.1. Pointwise estimates for strong solutions. 6.2. A sharp trace theorem. 6.3. Results from harmonic analysis. 6.4. Some further estimates for boundary value problems in a spherical cap. 6.5. L[symbol] estimates for solutions of constant coefficient problems in a spherical cap. 6.6. Local estimates for strong solutions of constant coefficient problems. 6.7. Local interior L[symbol] estimates for the second derivatives of strong solutions of differential equations. 6.8. Local L[symbol] second derivative estimates near the boundary. 6.9. Existence of strong solutions for the oblique derivative problem 7. Viscosity solutions of oblique derivative problems. 7.1. Definitions and notation. 7.2. The Theorem of Aleksandrov. 7.3. Preliminary results for the comparison theorem for viscosity solutions. 7.4. The comparison principle for viscosity sub- and supersolutions. 7.5. A test function construction for the oblique derivative problem. 7.6. The comparison principle for oblique derivative problems. 7.7. Existence and uniqueness of viscosity solutions -- 8. Pointwise bounds for solutions of problems with quasilinear equations. 8.1. Maximum estimates for nondivergence equations. 8.2. Hölder estimates for nondivergence equations. 8.3. Maximum estimates for conormal problems. 8.4. Hölder estimates for conormal problems -- - 9. Gradient estimates for general form oblique derivative problems. 9.1. Interior gradient bounds. 9.2. A simple boundary value problem. 9.3. Gradient estimates for general boundary conditions. General considerations. 9.4. Global gradient estimates for general boundary conditions and false mean curvature equations I. 9.5. Global gradient estimates for general boundary conditions and false mean curvature equations II. 9.6. Local gradient estimates. 9.7. Gradient estimates for capillary-type problems -- 10. Gradient estimates for the conormal derivative problems. 10.1. The Sobolev inequality of Michael and Simon. 10.2. The interior gradient bound. 10.3. Preliminaries for estimates. 10.4. Gradient bounds for the conormal problem -- - 11. Higher order estimates and existence of solutions for quasilinear oblique derivative problems. 11.1. The Hölder gradient estimate for conormal problems. 11.2. A solvability theorem. 11.3. Existence results and estimates for linear equations and nonlinear boundary conditions in spherical caps. 11.4. Estimates and existence results for linear equations and nonlinear boundary conditions in general domains. 11.5. Mixed boundary value problems for simple quasilinear differential equations and nonlinear boundary conditions in spherical caps. 11.6. Hölder gradient estimates for quasilinear equations. 11.7. A basic existence theorem for quasilinear elliptic equations with nonlinear boundary conditions. 11.8. Second derivative Hölder estimates. 11.9. Existence theorems for our examples -- - 12. Oblique derivative problems for fully nonlinear elliptic equations. 12.1. Maximum estimates, comparison principles, and a uniqueness theorem. 12.2. Second derivative Hölder estimates. 12.3. Second derivative Hölder estimates for solutions of oblique derivative problems. 12.4. Uniformly elliptic fully nonlinear problems This book gives an up-to-date exposition on the theory of oblique derivative problems for elliptic equations. The modern analysis of shock reflection was made possible by the theory of oblique derivative problems developed by the author. Such problems also arise in many other physical situations such as the shape of a capillary surface and problems of optimal transportation. We begin with basic results for linear oblique derivative problems and work through the theory for quasilinear and nonlinear problems. A final chapter discusses some of the applications. In addition, notes to each chapter give a history of the topics in that chapter and suggestions for further reading |
| Beschreibung: | 1 Online-Ressource |
| ISBN: | 1299556418 9781299556416 9789814452335 9789814452342 9814452335 9814452343 |
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| 100 | 1 | |a Lieberman, Gary M. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Oblique derivative problems for elliptic equations |c Gary M. Lieberman |
| 264 | 1 | |a Singapore |b World Scientific |c c2013 | |
| 300 | |a 1 Online-Ressource | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
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| 500 | |a Includes bibliographical references and index | ||
| 500 | |a 1. Pointwise estimates. 1.1. The maximum principle. 1.2. The definition of obliqueness. 1.3. The case c < 0, [symbol]. 1.4. A generalized change of variables formula. 1.5. The Aleksandrov-Bakel'man-Pucci maximum principles. 1.6. The interior weak Harnack inequality. 1.7. The weak Harnack inequality at the boundary. 1.8. The strong maximum principle and uniqueness. 1.9. Hölder continuity. 1.10. The local maximum principle. 1.11. Pointwise estimates for solutions of mixed boundary value problems. 1.12. Derivative bounds for solutions of elliptic equations -- 2. Classical Schauder theory from a modern perspective. 2.1. Definitions and properties of Hölder spaces. 2.2. An alternative characterization of Hölder spaces. 2.3. An existence result. 2.4. Basic interior estimates. 2.5. The Perron process for the Dirichlet problem. 2.6. A model mixed boundary value problem. 2.7. Domains with curved boundary. 2.8. Fredholm-Riesz-Schauder theory -- | ||
| 500 | |a - 3. The Miller barrier and some supersolutions for oblique derivative problems. 3.1. Theory of ordinary differential equations. 3.2. The Miller barrier construction. 3.3. Construction of supersolutions for Dirichlet data. 3.4. Construction of a supersolution for oblique derivative problems. 3.5. The strong maximum principle, revisited. 3.6. A Miller barrier for mixed boundary value problems -- 4. Hölder estimates for first and second derivatives. 4.1. C[symbol] estimates for continuous [symbol]. 4.2. Regularized distance. 4.3. Existence of solutions for continuous [symbol]. 4.4. Hölder gradient estimates for the Dirichlet problem. 4.5. C[symbol] estimates with discontinuous [symbol] in two dimensions. 4.6. C[symbol] estimates for discontinuous [symbol] in higher dimensions. 4.7. C[symbol] estimates -- | ||
| 500 | |a - 5. Weak solutions. 5.1. Definitions and basic properties of weak derivatives. 5.2. Sobolev imbedding theorems. 5.3. Poincaré's inequality. 5.4. The weak maximum principle. 5.5. Trace theorems. 5.6. Existence of weak solutions. 5.7. Higher regularity of solutions. 5.8. Global boundedness of weak solutions. 5.9. The local maximum principle. 5.10. The DeGiorgi class. 5.11. Membership of supersolutions in the De Giorgi class. 5.12. Consequences of the local estimates. 5.13. Integral characterizations of Hölder spaces. 5.14. Schauder estimates -- | ||
| 500 | |a - 6. Strong solutions. 6.1. Pointwise estimates for strong solutions. 6.2. A sharp trace theorem. 6.3. Results from harmonic analysis. 6.4. Some further estimates for boundary value problems in a spherical cap. 6.5. L[symbol] estimates for solutions of constant coefficient problems in a spherical cap. 6.6. Local estimates for strong solutions of constant coefficient problems. 6.7. Local interior L[symbol] estimates for the second derivatives of strong solutions of differential equations. 6.8. Local L[symbol] second derivative estimates near the boundary. 6.9. Existence of strong solutions for the oblique derivative problem | ||
| 500 | |a 7. Viscosity solutions of oblique derivative problems. 7.1. Definitions and notation. 7.2. The Theorem of Aleksandrov. 7.3. Preliminary results for the comparison theorem for viscosity solutions. 7.4. The comparison principle for viscosity sub- and supersolutions. 7.5. A test function construction for the oblique derivative problem. 7.6. The comparison principle for oblique derivative problems. 7.7. Existence and uniqueness of viscosity solutions -- 8. Pointwise bounds for solutions of problems with quasilinear equations. 8.1. Maximum estimates for nondivergence equations. 8.2. Hölder estimates for nondivergence equations. 8.3. Maximum estimates for conormal problems. 8.4. Hölder estimates for conormal problems -- | ||
| 500 | |a - 9. Gradient estimates for general form oblique derivative problems. 9.1. Interior gradient bounds. 9.2. A simple boundary value problem. 9.3. Gradient estimates for general boundary conditions. General considerations. 9.4. Global gradient estimates for general boundary conditions and false mean curvature equations I. 9.5. Global gradient estimates for general boundary conditions and false mean curvature equations II. 9.6. Local gradient estimates. 9.7. Gradient estimates for capillary-type problems -- 10. Gradient estimates for the conormal derivative problems. 10.1. The Sobolev inequality of Michael and Simon. 10.2. The interior gradient bound. 10.3. Preliminaries for estimates. 10.4. Gradient bounds for the conormal problem -- | ||
| 500 | |a - 11. Higher order estimates and existence of solutions for quasilinear oblique derivative problems. 11.1. The Hölder gradient estimate for conormal problems. 11.2. A solvability theorem. 11.3. Existence results and estimates for linear equations and nonlinear boundary conditions in spherical caps. 11.4. Estimates and existence results for linear equations and nonlinear boundary conditions in general domains. 11.5. Mixed boundary value problems for simple quasilinear differential equations and nonlinear boundary conditions in spherical caps. 11.6. Hölder gradient estimates for quasilinear equations. 11.7. A basic existence theorem for quasilinear elliptic equations with nonlinear boundary conditions. 11.8. Second derivative Hölder estimates. 11.9. Existence theorems for our examples -- | ||
| 500 | |a - 12. Oblique derivative problems for fully nonlinear elliptic equations. 12.1. Maximum estimates, comparison principles, and a uniqueness theorem. 12.2. Second derivative Hölder estimates. 12.3. Second derivative Hölder estimates for solutions of oblique derivative problems. 12.4. Uniformly elliptic fully nonlinear problems | ||
| 500 | |a This book gives an up-to-date exposition on the theory of oblique derivative problems for elliptic equations. The modern analysis of shock reflection was made possible by the theory of oblique derivative problems developed by the author. Such problems also arise in many other physical situations such as the shape of a capillary surface and problems of optimal transportation. We begin with basic results for linear oblique derivative problems and work through the theory for quasilinear and nonlinear problems. A final chapter discusses some of the applications. In addition, notes to each chapter give a history of the topics in that chapter and suggestions for further reading | ||
| 650 | 7 | |a MATHEMATICS / Differential Equations / Partial |2 bisacsh | |
| 650 | 7 | |a Differential equations, Elliptic |2 fast | |
| 650 | 4 | |a Mathematische Physik | |
| 650 | 4 | |a Mathematical physics | |
| 650 | 4 | |a Differential equations, Partial | |
| 650 | 0 | 7 | |a Elliptische Differentialgleichung |0 (DE-588)4014485-9 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
| _version_ | 1804175555495460864 |
|---|---|
| any_adam_object | |
| author | Lieberman, Gary M. |
| author_facet | Lieberman, Gary M. |
| author_role | aut |
| author_sort | Lieberman, Gary M. |
| author_variant | g m l gm gml |
| building | Verbundindex |
| bvnumber | BV043123675 |
| collection | ZDB-4-EBA |
| ctrlnum | (OCoLC)843871618 (DE-599)BVBBV043123675 |
| dewey-full | 515.353 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.353 |
| dewey-search | 515.353 |
| dewey-sort | 3515.353 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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Lieberman</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Singapore</subfield><subfield code="b">World Scientific</subfield><subfield code="c">c2013</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 Online-Ressource</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Includes bibliographical references and index</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">1. Pointwise estimates. 1.1. The maximum principle. 1.2. The definition of obliqueness. 1.3. The case c < 0, [symbol]. 1.4. 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Trace theorems. 5.6. Existence of weak solutions. 5.7. Higher regularity of solutions. 5.8. Global boundedness of weak solutions. 5.9. The local maximum principle. 5.10. The DeGiorgi class. 5.11. Membership of supersolutions in the De Giorgi class. 5.12. Consequences of the local estimates. 5.13. Integral characterizations of Hölder spaces. 5.14. Schauder estimates -- </subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a"> - 6. Strong solutions. 6.1. Pointwise estimates for strong solutions. 6.2. A sharp trace theorem. 6.3. Results from harmonic analysis. 6.4. Some further estimates for boundary value problems in a spherical cap. 6.5. L[symbol] estimates for solutions of constant coefficient problems in a spherical cap. 6.6. Local estimates for strong solutions of constant coefficient problems. 6.7. Local interior L[symbol] estimates for the second derivatives of strong solutions of differential equations. 6.8. Local L[symbol] second derivative estimates near the boundary. 6.9. Existence of strong solutions for the oblique derivative problem</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">7. Viscosity solutions of oblique derivative problems. 7.1. Definitions and notation. 7.2. The Theorem of Aleksandrov. 7.3. Preliminary results for the comparison theorem for viscosity solutions. 7.4. The comparison principle for viscosity sub- and supersolutions. 7.5. A test function construction for the oblique derivative problem. 7.6. The comparison principle for oblique derivative problems. 7.7. Existence and uniqueness of viscosity solutions -- 8. Pointwise bounds for solutions of problems with quasilinear equations. 8.1. Maximum estimates for nondivergence equations. 8.2. Hölder estimates for nondivergence equations. 8.3. Maximum estimates for conormal problems. 8.4. Hölder estimates for conormal problems -- </subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a"> - 9. Gradient estimates for general form oblique derivative problems. 9.1. Interior gradient bounds. 9.2. A simple boundary value problem. 9.3. Gradient estimates for general boundary conditions. General considerations. 9.4. Global gradient estimates for general boundary conditions and false mean curvature equations I. 9.5. Global gradient estimates for general boundary conditions and false mean curvature equations II. 9.6. Local gradient estimates. 9.7. Gradient estimates for capillary-type problems -- 10. Gradient estimates for the conormal derivative problems. 10.1. The Sobolev inequality of Michael and Simon. 10.2. The interior gradient bound. 10.3. Preliminaries for estimates. 10.4. Gradient bounds for the conormal problem -- </subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a"> - 11. Higher order estimates and existence of solutions for quasilinear oblique derivative problems. 11.1. The Hölder gradient estimate for conormal problems. 11.2. A solvability theorem. 11.3. Existence results and estimates for linear equations and nonlinear boundary conditions in spherical caps. 11.4. Estimates and existence results for linear equations and nonlinear boundary conditions in general domains. 11.5. Mixed boundary value problems for simple quasilinear differential equations and nonlinear boundary conditions in spherical caps. 11.6. Hölder gradient estimates for quasilinear equations. 11.7. A basic existence theorem for quasilinear elliptic equations with nonlinear boundary conditions. 11.8. Second derivative Hölder estimates. 11.9. Existence theorems for our examples -- </subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a"> - 12. Oblique derivative problems for fully nonlinear elliptic equations. 12.1. Maximum estimates, comparison principles, and a uniqueness theorem. 12.2. Second derivative Hölder estimates. 12.3. Second derivative Hölder estimates for solutions of oblique derivative problems. 12.4. Uniformly elliptic fully nonlinear problems</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">This book gives an up-to-date exposition on the theory of oblique derivative problems for elliptic equations. The modern analysis of shock reflection was made possible by the theory of oblique derivative problems developed by the author. Such problems also arise in many other physical situations such as the shape of a capillary surface and problems of optimal transportation. We begin with basic results for linear oblique derivative problems and work through the theory for quasilinear and nonlinear problems. A final chapter discusses some of the applications. 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| id | DE-604.BV043123675 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:18:09Z |
| institution | BVB |
| isbn | 1299556418 9781299556416 9789814452335 9789814452342 9814452335 9814452343 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-028547865 |
| oclc_num | 843871618 |
| open_access_boolean | |
| owner | DE-1046 DE-1047 |
| owner_facet | DE-1046 DE-1047 |
| physical | 1 Online-Ressource |
| psigel | ZDB-4-EBA ZDB-4-EBA FAW_PDA_EBA |
| publishDate | 2013 |
| publishDateSearch | 2013 |
| publishDateSort | 2013 |
| publisher | World Scientific |
| record_format | marc |
| spelling | Lieberman, Gary M. Verfasser aut Oblique derivative problems for elliptic equations Gary M. Lieberman Singapore World Scientific c2013 1 Online-Ressource txt rdacontent c rdamedia cr rdacarrier Includes bibliographical references and index 1. Pointwise estimates. 1.1. The maximum principle. 1.2. The definition of obliqueness. 1.3. The case c < 0, [symbol]. 1.4. A generalized change of variables formula. 1.5. The Aleksandrov-Bakel'man-Pucci maximum principles. 1.6. The interior weak Harnack inequality. 1.7. The weak Harnack inequality at the boundary. 1.8. The strong maximum principle and uniqueness. 1.9. Hölder continuity. 1.10. The local maximum principle. 1.11. Pointwise estimates for solutions of mixed boundary value problems. 1.12. Derivative bounds for solutions of elliptic equations -- 2. Classical Schauder theory from a modern perspective. 2.1. Definitions and properties of Hölder spaces. 2.2. An alternative characterization of Hölder spaces. 2.3. An existence result. 2.4. Basic interior estimates. 2.5. The Perron process for the Dirichlet problem. 2.6. A model mixed boundary value problem. 2.7. Domains with curved boundary. 2.8. Fredholm-Riesz-Schauder theory -- - 3. The Miller barrier and some supersolutions for oblique derivative problems. 3.1. Theory of ordinary differential equations. 3.2. The Miller barrier construction. 3.3. Construction of supersolutions for Dirichlet data. 3.4. Construction of a supersolution for oblique derivative problems. 3.5. The strong maximum principle, revisited. 3.6. A Miller barrier for mixed boundary value problems -- 4. Hölder estimates for first and second derivatives. 4.1. C[symbol] estimates for continuous [symbol]. 4.2. Regularized distance. 4.3. Existence of solutions for continuous [symbol]. 4.4. Hölder gradient estimates for the Dirichlet problem. 4.5. C[symbol] estimates with discontinuous [symbol] in two dimensions. 4.6. C[symbol] estimates for discontinuous [symbol] in higher dimensions. 4.7. C[symbol] estimates -- - 5. Weak solutions. 5.1. Definitions and basic properties of weak derivatives. 5.2. Sobolev imbedding theorems. 5.3. Poincaré's inequality. 5.4. The weak maximum principle. 5.5. Trace theorems. 5.6. Existence of weak solutions. 5.7. Higher regularity of solutions. 5.8. Global boundedness of weak solutions. 5.9. The local maximum principle. 5.10. The DeGiorgi class. 5.11. Membership of supersolutions in the De Giorgi class. 5.12. Consequences of the local estimates. 5.13. Integral characterizations of Hölder spaces. 5.14. Schauder estimates -- - 6. Strong solutions. 6.1. Pointwise estimates for strong solutions. 6.2. A sharp trace theorem. 6.3. Results from harmonic analysis. 6.4. Some further estimates for boundary value problems in a spherical cap. 6.5. L[symbol] estimates for solutions of constant coefficient problems in a spherical cap. 6.6. Local estimates for strong solutions of constant coefficient problems. 6.7. Local interior L[symbol] estimates for the second derivatives of strong solutions of differential equations. 6.8. Local L[symbol] second derivative estimates near the boundary. 6.9. Existence of strong solutions for the oblique derivative problem 7. Viscosity solutions of oblique derivative problems. 7.1. Definitions and notation. 7.2. The Theorem of Aleksandrov. 7.3. Preliminary results for the comparison theorem for viscosity solutions. 7.4. The comparison principle for viscosity sub- and supersolutions. 7.5. A test function construction for the oblique derivative problem. 7.6. The comparison principle for oblique derivative problems. 7.7. Existence and uniqueness of viscosity solutions -- 8. Pointwise bounds for solutions of problems with quasilinear equations. 8.1. Maximum estimates for nondivergence equations. 8.2. Hölder estimates for nondivergence equations. 8.3. Maximum estimates for conormal problems. 8.4. Hölder estimates for conormal problems -- - 9. Gradient estimates for general form oblique derivative problems. 9.1. Interior gradient bounds. 9.2. A simple boundary value problem. 9.3. Gradient estimates for general boundary conditions. General considerations. 9.4. Global gradient estimates for general boundary conditions and false mean curvature equations I. 9.5. Global gradient estimates for general boundary conditions and false mean curvature equations II. 9.6. Local gradient estimates. 9.7. Gradient estimates for capillary-type problems -- 10. Gradient estimates for the conormal derivative problems. 10.1. The Sobolev inequality of Michael and Simon. 10.2. The interior gradient bound. 10.3. Preliminaries for estimates. 10.4. Gradient bounds for the conormal problem -- - 11. Higher order estimates and existence of solutions for quasilinear oblique derivative problems. 11.1. The Hölder gradient estimate for conormal problems. 11.2. A solvability theorem. 11.3. Existence results and estimates for linear equations and nonlinear boundary conditions in spherical caps. 11.4. Estimates and existence results for linear equations and nonlinear boundary conditions in general domains. 11.5. Mixed boundary value problems for simple quasilinear differential equations and nonlinear boundary conditions in spherical caps. 11.6. Hölder gradient estimates for quasilinear equations. 11.7. A basic existence theorem for quasilinear elliptic equations with nonlinear boundary conditions. 11.8. Second derivative Hölder estimates. 11.9. Existence theorems for our examples -- - 12. Oblique derivative problems for fully nonlinear elliptic equations. 12.1. Maximum estimates, comparison principles, and a uniqueness theorem. 12.2. Second derivative Hölder estimates. 12.3. Second derivative Hölder estimates for solutions of oblique derivative problems. 12.4. Uniformly elliptic fully nonlinear problems This book gives an up-to-date exposition on the theory of oblique derivative problems for elliptic equations. The modern analysis of shock reflection was made possible by the theory of oblique derivative problems developed by the author. Such problems also arise in many other physical situations such as the shape of a capillary surface and problems of optimal transportation. We begin with basic results for linear oblique derivative problems and work through the theory for quasilinear and nonlinear problems. A final chapter discusses some of the applications. In addition, notes to each chapter give a history of the topics in that chapter and suggestions for further reading MATHEMATICS / Differential Equations / Partial bisacsh Differential equations, Elliptic fast Mathematische Physik Mathematical physics Differential equations, Partial Elliptische Differentialgleichung (DE-588)4014485-9 gnd rswk-swf Elliptische Differentialgleichung (DE-588)4014485-9 s 1\p DE-604 Erscheint auch als Druckausgabe 978-981-4452-32-8 Erscheint auch als Druckausgabe 981-4452-32-7 http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=575398 Aggregator Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Lieberman, Gary M. Oblique derivative problems for elliptic equations MATHEMATICS / Differential Equations / Partial bisacsh Differential equations, Elliptic fast Mathematische Physik Mathematical physics Differential equations, Partial Elliptische Differentialgleichung (DE-588)4014485-9 gnd |
| subject_GND | (DE-588)4014485-9 |
| title | Oblique derivative problems for elliptic equations |
| title_auth | Oblique derivative problems for elliptic equations |
| title_exact_search | Oblique derivative problems for elliptic equations |
| title_full | Oblique derivative problems for elliptic equations Gary M. Lieberman |
| title_fullStr | Oblique derivative problems for elliptic equations Gary M. Lieberman |
| title_full_unstemmed | Oblique derivative problems for elliptic equations Gary M. Lieberman |
| title_short | Oblique derivative problems for elliptic equations |
| title_sort | oblique derivative problems for elliptic equations |
| topic | MATHEMATICS / Differential Equations / Partial bisacsh Differential equations, Elliptic fast Mathematische Physik Mathematical physics Differential equations, Partial Elliptische Differentialgleichung (DE-588)4014485-9 gnd |
| topic_facet | MATHEMATICS / Differential Equations / Partial Differential equations, Elliptic Mathematische Physik Mathematical physics Differential equations, Partial Elliptische Differentialgleichung |
| url | http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=575398 |
| work_keys_str_mv | AT liebermangarym obliquederivativeproblemsforellipticequations |