The Hodge-Laplacian: boundary value problems on Riemannian manifolds
The core of this monograph is the development of tools to derive well-posedness results in very general geometric settings for elliptic differential operators. A new generation of Calderón-Zygmund theory is developed for variable coefficient singular integral operators, which turns out to be particu...
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| Main Authors: | , , , |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Berlin ; Boston
De Gruyter
[2016]
|
| Series: | De Gruyter studies in mathematics
64 |
| Subjects: | |
| Online Access: | DE-898 DE-91 Volltext |
| Summary: | The core of this monograph is the development of tools to derive well-posedness results in very general geometric settings for elliptic differential operators. A new generation of Calderón-Zygmund theory is developed for variable coefficient singular integral operators, which turns out to be particularly versatile in dealing with boundary value problems for the Hodge-Laplacian on uniformly rectifiable subdomains of Riemannian manifolds via boundary layer methods. In addition to absolute and relative boundary conditions for differential forms, this monograph treats the Hodge-Laplacian equipped with classical Dirichlet, Neumann, Transmission, Poincaré, and Robin boundary conditions in regular Semmes-Kenig-Toro domains.Lying at the intersection of partial differential equations, harmonic analysis, and differential geometry, this text is suitable for a wide range of PhD students, researchers, and professionals. Contents:PrefaceIntroduction and Statement of Main ResultsGeometric Concepts and ToolsHarmonic Layer Potentials Associated with the Hodge-de Rham Formalism on UR DomainsHarmonic Layer Potentials Associated with the Levi-Civita Connection on UR DomainsDirichlet and Neumann Boundary Value Problems for the Hodge-Laplacian on Regular SKT DomainsFatou Theorems and Integral Representations for the Hodge-Laplacian on Regular SKT DomainsSolvability of Boundary Problems for the Hodge-Laplacian in the Hodge-de Rham FormalismAdditional Results and ApplicationsFurther Tools from Differential Geometry, Harmonic Analysis, Geometric Measure Theory, Functional Analysis, Partial Differential Equations, and Clifford AnalysisBibliographyIndex |
| Item Description: | Description based on online resource; title from PDF title page (publisher's Web site, viewed Sep. 08, 2016) |
| Physical Description: | 1 online resource (528pages) |
| ISBN: | 9783110484380 9783110482669 |
| DOI: | 10.1515/9783110484380 |
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| 520 | |a The core of this monograph is the development of tools to derive well-posedness results in very general geometric settings for elliptic differential operators. A new generation of Calderón-Zygmund theory is developed for variable coefficient singular integral operators, which turns out to be particularly versatile in dealing with boundary value problems for the Hodge-Laplacian on uniformly rectifiable subdomains of Riemannian manifolds via boundary layer methods. In addition to absolute and relative boundary conditions for differential forms, this monograph treats the Hodge-Laplacian equipped with classical Dirichlet, Neumann, Transmission, Poincaré, and Robin boundary conditions in regular Semmes-Kenig-Toro domains.Lying at the intersection of partial differential equations, harmonic analysis, and differential geometry, this text is suitable for a wide range of PhD students, researchers, and professionals. Contents:PrefaceIntroduction and Statement of Main ResultsGeometric Concepts and ToolsHarmonic Layer Potentials Associated with the Hodge-de Rham Formalism on UR DomainsHarmonic Layer Potentials Associated with the Levi-Civita Connection on UR DomainsDirichlet and Neumann Boundary Value Problems for the Hodge-Laplacian on Regular SKT DomainsFatou Theorems and Integral Representations for the Hodge-Laplacian on Regular SKT DomainsSolvability of Boundary Problems for the Hodge-Laplacian in the Hodge-de Rham FormalismAdditional Results and ApplicationsFurther Tools from Differential Geometry, Harmonic Analysis, Geometric Measure Theory, Functional Analysis, Partial Differential Equations, and Clifford AnalysisBibliographyIndex | ||
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| id | DE-604.BV043867770 |
| illustrated | Not Illustrated |
| indexdate | 2025-03-25T15:01:56Z |
| institution | BVB |
| isbn | 9783110484380 9783110482669 |
| language | English |
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| publishDate | 2016 |
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| publisher | De Gruyter |
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| series | De Gruyter studies in mathematics |
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| spelling | Mitrea, Dorina 1965- (DE-588)140077642 aut The Hodge-Laplacian boundary value problems on Riemannian manifolds Dorina Mitrea, Irina Mitrea, Marius Mitrea, Michael Taylor Berlin ; Boston De Gruyter [2016] © 2016 1 online resource (528pages) txt rdacontent c rdamedia cr rdacarrier De Gruyter studies in mathematics 64 Description based on online resource; title from PDF title page (publisher's Web site, viewed Sep. 08, 2016) The core of this monograph is the development of tools to derive well-posedness results in very general geometric settings for elliptic differential operators. A new generation of Calderón-Zygmund theory is developed for variable coefficient singular integral operators, which turns out to be particularly versatile in dealing with boundary value problems for the Hodge-Laplacian on uniformly rectifiable subdomains of Riemannian manifolds via boundary layer methods. In addition to absolute and relative boundary conditions for differential forms, this monograph treats the Hodge-Laplacian equipped with classical Dirichlet, Neumann, Transmission, Poincaré, and Robin boundary conditions in regular Semmes-Kenig-Toro domains.Lying at the intersection of partial differential equations, harmonic analysis, and differential geometry, this text is suitable for a wide range of PhD students, researchers, and professionals. Contents:PrefaceIntroduction and Statement of Main ResultsGeometric Concepts and ToolsHarmonic Layer Potentials Associated with the Hodge-de Rham Formalism on UR DomainsHarmonic Layer Potentials Associated with the Levi-Civita Connection on UR DomainsDirichlet and Neumann Boundary Value Problems for the Hodge-Laplacian on Regular SKT DomainsFatou Theorems and Integral Representations for the Hodge-Laplacian on Regular SKT DomainsSolvability of Boundary Problems for the Hodge-Laplacian in the Hodge-de Rham FormalismAdditional Results and ApplicationsFurther Tools from Differential Geometry, Harmonic Analysis, Geometric Measure Theory, Functional Analysis, Partial Differential Equations, and Clifford AnalysisBibliographyIndex In English Laplace-Operator Riemannscher Raum Randwertproblem (DE-588)4048395-2 gnd rswk-swf Laplace-Operator (DE-588)4166772-4 gnd rswk-swf Riemannscher Raum (DE-588)4128295-4 gnd rswk-swf Laplace-Operator (DE-588)4166772-4 s Randwertproblem (DE-588)4048395-2 s Riemannscher Raum (DE-588)4128295-4 s DE-604 Mitrea, Irina aut Mitrea, Marius (DE-588)1026933625 aut Taylor, Michael Eugene 1946- (DE-588)123980119 aut Erscheint auch als Druck-Ausgabe 978-3-11-048266-9 De Gruyter studies in mathematics 64 (DE-604)BV044966417 64 https://doi.org/10.1515/9783110484380 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Mitrea, Dorina 1965- Mitrea, Irina Mitrea, Marius Taylor, Michael Eugene 1946- The Hodge-Laplacian boundary value problems on Riemannian manifolds De Gruyter studies in mathematics Laplace-Operator Riemannscher Raum Randwertproblem (DE-588)4048395-2 gnd Laplace-Operator (DE-588)4166772-4 gnd Riemannscher Raum (DE-588)4128295-4 gnd |
| subject_GND | (DE-588)4048395-2 (DE-588)4166772-4 (DE-588)4128295-4 |
| title | The Hodge-Laplacian boundary value problems on Riemannian manifolds |
| title_auth | The Hodge-Laplacian boundary value problems on Riemannian manifolds |
| title_exact_search | The Hodge-Laplacian boundary value problems on Riemannian manifolds |
| title_full | The Hodge-Laplacian boundary value problems on Riemannian manifolds Dorina Mitrea, Irina Mitrea, Marius Mitrea, Michael Taylor |
| title_fullStr | The Hodge-Laplacian boundary value problems on Riemannian manifolds Dorina Mitrea, Irina Mitrea, Marius Mitrea, Michael Taylor |
| title_full_unstemmed | The Hodge-Laplacian boundary value problems on Riemannian manifolds Dorina Mitrea, Irina Mitrea, Marius Mitrea, Michael Taylor |
| title_short | The Hodge-Laplacian |
| title_sort | the hodge laplacian boundary value problems on riemannian manifolds |
| title_sub | boundary value problems on Riemannian manifolds |
| topic | Laplace-Operator Riemannscher Raum Randwertproblem (DE-588)4048395-2 gnd Laplace-Operator (DE-588)4166772-4 gnd Riemannscher Raum (DE-588)4128295-4 gnd |
| topic_facet | Laplace-Operator Riemannscher Raum Randwertproblem |
| url | https://doi.org/10.1515/9783110484380 |
| volume_link | (DE-604)BV044966417 |
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