Elliptic problems in nonsmooth domains:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Philadelphia, Pa.
SIAM, Society for Industrial and Applied Mathematics
2011
|
| Ausgabe: | Republ. of the work first publ. by Pitman ... 1985 |
| Schriftenreihe: | Classics in Applied Mathematics
69 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XX, 410 S. graph. Darst. |
| ISBN: | 9781611972023 |
Internformat
MARC
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| 100 | 1 | |a Grisvard, Pierre |d 1940-1994 |e Verfasser |0 (DE-588)143537202 |4 aut | |
| 245 | 1 | 0 | |a Elliptic problems in nonsmooth domains |c Pierre Grisvard |
| 250 | |a Republ. of the work first publ. by Pitman ... 1985 | ||
| 264 | 1 | |a Philadelphia, Pa. |b SIAM, Society for Industrial and Applied Mathematics |c 2011 | |
| 300 | |a XX, 410 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Classics in Applied Mathematics |v 69 | |
| 534 | |c 1985 | ||
| 650 | 4 | |a Problèmes aux limites - Solutions numériques | |
| 650 | 4 | |a Équations différentielles elliptiques - Solutions numériques | |
| 650 | 4 | |a Boundary value problems |x Numerical solutions | |
| 650 | 4 | |a Differential equations, Elliptic |x Numerical solutions | |
| 650 | 0 | 7 | |a Elliptisches Randwertproblem |0 (DE-588)4193399-0 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Randwertproblem |0 (DE-588)4048395-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Elliptische Differentialgleichung |0 (DE-588)4014485-9 |2 gnd |9 rswk-swf |
| 651 | 4 | |a Rome - History - Republic, 265-30 B.C | |
| 651 | 4 | |a Rom | |
| 689 | 0 | 0 | |a Elliptische Differentialgleichung |0 (DE-588)4014485-9 |D s |
| 689 | 0 | 1 | |a Randwertproblem |0 (DE-588)4048395-2 |D s |
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| 689 | 1 | 0 | |a Elliptisches Randwertproblem |0 (DE-588)4193399-0 |D s |
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| 775 | 0 | 8 | |i Reproduktion von |d Boston : Pitman, 1985 |z 0-273-08647-2 |w (DE-604)BV006518815 |
| 830 | 0 | |a Classics in Applied Mathematics |v 69 |w (DE-604)BV008258410 |9 69 | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-024722978 | ||
Datensatz im Suchindex
| _version_ | 1804148802433581056 |
|---|---|
| adam_text | Contents
Foreword xiii
Preface xv
1 Sobolev spaces 1
1.1 Motivation 1
1.2 Boundaries 4
1.2.1 Graphs and manifolds 5
1.2.2 Segment property and cone property 10
1.3 Spaces 14
1.3.1 Euclidean space 14
1.3.2 Open subsets of the Euclidean space 16
1.3.3 Manifolds 19
1.4 Basic properties 20
1.4.1 Multiplication and differentiation 20
1.4.2 Density results 24
1.4.3 Continuation, compactness and convexity
inequalities 25
1.4.4 Imbeddings 27
1.4.5 Spaces defined on polygons 33
1.5 Traces 36
1.5.1 Hyperplanes 36
1.5.2 Polygons 42
1.5.3 Maximal domains of elliptic operators 52
1.6 Boundary conditions 62
1.6.1 Normal systems 62
1.7 A model domain with a cut 74
2 Regular second-order elliptic boundary value problems 81
2.1 Foreword 84
2.2 Variational solution of special problems 84
2.2.1 Existence and uniqueness 84
2.2.2 Smoothness 87
IX
X
CONTENTS
2.3 A priori estimates 92
2.3.1 An inequality based on the duality mapping 92
2.3.2 An inequality in the half space 97
2.3.3 A general a priori estimate 105
2.4 Existence and uniqueness, the general case 111
2.4.1 The basic result 111
2.4.2 Applications of the Fredholm theory and
the maximum principle 119
2.5 Other kinds of solutions 128
2.5.1 More on smoothness 128
2.5.2 Very weak solution 129
3 Second-order elliptic boundary value problems in convex
domains 132
3.1 A priori estimates and the curvature of the boundary 132
3.1.1 An identity based on integration by parts 133
3.1.2 A priori inequalities for the Laplace operator
revisited 138
3.1.3 A priori inequalities for more general operators 142
3.2 Boundary value problems in convex domains 147
3.2.1 Linear boundary conditions 147
3.2.2 Nonlinear boundary conditions (review) 151
3.2.3 Nonlinear boundary conditions (continued) 156
3.2.4 Oblique boundary conditions 167
3.3 Boundary value problems in domains with turning points 174
4 Second-order elliptic boundary value problems in polygons 182
4.1 Foreword 182
4.2 A priori estimates in an infinite strip 184
4.2.1 Explicit solution by Fourier transform and
consequences 184
4.2.2 Lp bounds for the second derivatives of the
solution 189
4.3 Bounds in a polygon 194
4.3.1 The L2 case 194
4.3.2 The Lp case (p^2) 199
4.4 The Fredholm alternative 208
4.4.1 The semi-Fredholm properties 208
4.4.2 The adjoint problem 217
4.4.3 The Fredholm alternative for variational
problems 226
4.4.4 The Fredholm alternative for non variational
problems 234
CONTENTS
xi
5 More singular solutions 249
5.1 Behaviour of the derivatives of order higher than two 249
5.1.1 Special data 250
5.1.2 A trace theorem 256
5.1.3 More singular solutions 261
5.2 Operators with variable coefficients 265
6 Results in spaces of Holder functions 274
6.1 Foreword 274
6.2 A brief review of Holder spaces 275
6.3 Regular second-order elliptic boundary value problems
revisited 282
6.3.1 The Schauder inequality 282
6.3.2 Smoothness 287
6.4 Second-order elliptic problems in polygons revisited 289
6.4.1 The Schauder inequality in an infinite strip 289
6.4.2 The Schauder inequality in a polygon and its
consequences 295
7 A model fourth-order problem 301
7.1 Introductory results 301
7.2 Singular solutions, the L2 case 305
7.2.1 Kondratiev’s method in weighted spaces 305
7.2.2 Getting rid of the weights 321
7.3 Singular solutions, the Lr case 328
7.3.1 A priori inequalities 328
7.3.2 Smoothness 335
7.3.3 The related Stokes problem 340
8 Miscellaneous 345
8.1 The Dirichlet problem for a strongly nonlinear equation 345
8.2 Some three-dimensional results (an outline) 356
8.2.1 Edges 357
8.2.2 Conical points and vertices 361
8.3 The heat equation 372
8.4 The numerical solution of elliptic problems with
singularities 384
8.4.1 Weighted spaces and mesh refinements 384
8.4.2 Augmenting the space of trial functions 394
8.4.3 Calculating the stress intensity factor 396
Bibliography 400
Index 409
|
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| discipline | Mathematik |
| edition | Republ. of the work first publ. by Pitman ... 1985 |
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| geographic | Rome - History - Republic, 265-30 B.C Rom |
| geographic_facet | Rome - History - Republic, 265-30 B.C Rom |
| id | DE-604.BV039863470 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T00:12:55Z |
| institution | BVB |
| isbn | 9781611972023 |
| language | English |
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| physical | XX, 410 S. graph. Darst. |
| publishDate | 2011 |
| publishDateSearch | 2011 |
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| publisher | SIAM, Society for Industrial and Applied Mathematics |
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| series | Classics in Applied Mathematics |
| series2 | Classics in Applied Mathematics |
| spelling | Grisvard, Pierre 1940-1994 Verfasser (DE-588)143537202 aut Elliptic problems in nonsmooth domains Pierre Grisvard Republ. of the work first publ. by Pitman ... 1985 Philadelphia, Pa. SIAM, Society for Industrial and Applied Mathematics 2011 XX, 410 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Classics in Applied Mathematics 69 1985 Problèmes aux limites - Solutions numériques Équations différentielles elliptiques - Solutions numériques Boundary value problems Numerical solutions Differential equations, Elliptic Numerical solutions Elliptisches Randwertproblem (DE-588)4193399-0 gnd rswk-swf Randwertproblem (DE-588)4048395-2 gnd rswk-swf Elliptische Differentialgleichung (DE-588)4014485-9 gnd rswk-swf Rome - History - Republic, 265-30 B.C Rom Elliptische Differentialgleichung (DE-588)4014485-9 s Randwertproblem (DE-588)4048395-2 s DE-604 Elliptisches Randwertproblem (DE-588)4193399-0 s Reproduktion von Boston : Pitman, 1985 0-273-08647-2 (DE-604)BV006518815 Classics in Applied Mathematics 69 (DE-604)BV008258410 69 Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024722978&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Grisvard, Pierre 1940-1994 Elliptic problems in nonsmooth domains Classics in Applied Mathematics Problèmes aux limites - Solutions numériques Équations différentielles elliptiques - Solutions numériques Boundary value problems Numerical solutions Differential equations, Elliptic Numerical solutions Elliptisches Randwertproblem (DE-588)4193399-0 gnd Randwertproblem (DE-588)4048395-2 gnd Elliptische Differentialgleichung (DE-588)4014485-9 gnd |
| subject_GND | (DE-588)4193399-0 (DE-588)4048395-2 (DE-588)4014485-9 |
| title | Elliptic problems in nonsmooth domains |
| title_auth | Elliptic problems in nonsmooth domains |
| title_exact_search | Elliptic problems in nonsmooth domains |
| title_full | Elliptic problems in nonsmooth domains Pierre Grisvard |
| title_fullStr | Elliptic problems in nonsmooth domains Pierre Grisvard |
| title_full_unstemmed | Elliptic problems in nonsmooth domains Pierre Grisvard |
| title_short | Elliptic problems in nonsmooth domains |
| title_sort | elliptic problems in nonsmooth domains |
| topic | Problèmes aux limites - Solutions numériques Équations différentielles elliptiques - Solutions numériques Boundary value problems Numerical solutions Differential equations, Elliptic Numerical solutions Elliptisches Randwertproblem (DE-588)4193399-0 gnd Randwertproblem (DE-588)4048395-2 gnd Elliptische Differentialgleichung (DE-588)4014485-9 gnd |
| topic_facet | Problèmes aux limites - Solutions numériques Équations différentielles elliptiques - Solutions numériques Boundary value problems Numerical solutions Differential equations, Elliptic Numerical solutions Elliptisches Randwertproblem Randwertproblem Elliptische Differentialgleichung Rome - History - Republic, 265-30 B.C Rom |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024722978&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV008258410 |
| work_keys_str_mv | AT grisvardpierre ellipticproblemsinnonsmoothdomains |