The Dirichlet problem for the Laplacian in bounded and unbounded domains: a new approach to weak, strong and (2+k)-solutions in Sobolev-type spaces
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Harlow, Essex
Longman
1996
|
| Schriftenreihe: | Pitman research notes in mathematics series
360 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | 294 S. |
| ISBN: | 0582209536 |
Internformat
MARC
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| 100 | 1 | |a Simader, Christian G. |d 1943-2019 |e Verfasser |0 (DE-588)133701336 |4 aut | |
| 245 | 1 | 0 | |a The Dirichlet problem for the Laplacian in bounded and unbounded domains |b a new approach to weak, strong and (2+k)-solutions in Sobolev-type spaces |c C. G. Simader and H. Sohr |
| 264 | 1 | |a Harlow, Essex |b Longman |c 1996 | |
| 300 | |a 294 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Pitman research notes in mathematics series |v 360 | |
| 650 | 7 | |a Dirichlet, Problème de |2 ram | |
| 650 | 7 | |a EDP |2 inriac | |
| 650 | 7 | |a Laplace-vergelijking |2 gtt | |
| 650 | 7 | |a Partiële differentiaalvergelijkingen |2 gtt | |
| 650 | 7 | |a Sobolev ruimten |2 gtt | |
| 650 | 7 | |a espace Sobolev |2 inriac | |
| 650 | 7 | |a problème Dirichlet |2 inriac | |
| 650 | 7 | |a équation Laplace |2 inriac | |
| 650 | 4 | |a Dirichlet problem | |
| 650 | 0 | 7 | |a Dirichlet-Problem |0 (DE-588)4129762-3 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Laplace-Differentialgleichung |0 (DE-588)4228351-6 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Laplace-Differentialgleichung |0 (DE-588)4228351-6 |D s |
| 689 | 0 | 1 | |a Dirichlet-Problem |0 (DE-588)4129762-3 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Sohr, Hermann |e Verfasser |0 (DE-588)106421379 |4 aut | |
| 830 | 0 | |a Pitman research notes in mathematics series |v 360 |w (DE-604)BV000022845 |9 360 | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-007500446 | ||
Datensatz im Suchindex
| _version_ | 1804125680088121344 |
|---|---|
| adam_text | Contents
Preface 3
Introduction 6
Chapter I: Sobolev type spaces for the weak Dirichlet problem in Lq 24
1 The appropriate Sobolev spaces Hl 9(G) 24
2 Properties of the spaces #0M(G) and Hlq{G) 27
3 An asymptotic representation for functions harmonic in an exterior domain
with L? gradients 37
Chapter II: The weak Dirichlet problem for A in Lq in bounded and exterior
domains 45
1 A variational inequality in Hl q(G) and a corresponding functional repres¬
entation. Introduction 45
2 Local estimates and regularity 49
3 Uniqueness 62
4 Proof of the main theorem (Theorem 1.1) 64
5 L regularity theorems 66
6 Harmonic functions h £ Hl q{G) in exterior domains 68
7 Variational inequalities and functional representations in //q 9(G) for exterior
domains 73
8 Higher derivatives 85
9 Certain strong solutions of the non homogeneous equation — A p = f .... 94
10 The Dirichlet problem for Ap = 0 in bounded and exterior domains 98
11 A second look at the non homogeneous equation. The boundary value at
infinity for 1 q n 110
12 Direct determination of the constant Cq 0 in the variational inequality (1.1)113
Chapter III: Strong solutions of the Dirichlet problem in exterior domains 128
1 Introduction 128
2 Technical preliminaries. The appropriate Sobolev spaces 130
3 The null space of the strong Dirichlet problem in an exterior domain .... 160
4 Strong L solutions of A u = / in the whole space R for 1 q oo ... 169
5 Strong L solutions of the Dirichlet problem — A u = /, u aG = 0 in an
exterior domain 171
1
Chapter IV: (2 + fc) solutions of the Dirichlet problem in exterior domains 177
1 Introduction 177
2 Harmonic polynomials 180
3 The appropriate Sobolev spaces 201
4 An asymptotic representation for functions being harmonic in an exterior
domain having higher order derivatives in L9 235
5 The null space of the Dirichlet problem in H2^Kq(G) 245
6 (2 + /^ solutions in the whole space Rn 252
6.1 Polynomial data and solutions 252
6.2 Solutions in the spaces H2+k i{Rn; Go) 254
7 (2 + fc) solutions of the Dirichlet problem in exterior domains 262
Appendix 283
List of symbols and notations 287
Bibliography 291
2 CONTENTS
|
| any_adam_object | 1 |
| author | Simader, Christian G. 1943-2019 Sohr, Hermann |
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| dewey-ones | 515 - Analysis |
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| id | DE-604.BV011184672 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:05:24Z |
| institution | BVB |
| isbn | 0582209536 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007500446 |
| oclc_num | 27429788 |
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| physical | 294 S. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
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| publisher | Longman |
| record_format | marc |
| series | Pitman research notes in mathematics series |
| series2 | Pitman research notes in mathematics series |
| spelling | Simader, Christian G. 1943-2019 Verfasser (DE-588)133701336 aut The Dirichlet problem for the Laplacian in bounded and unbounded domains a new approach to weak, strong and (2+k)-solutions in Sobolev-type spaces C. G. Simader and H. Sohr Harlow, Essex Longman 1996 294 S. txt rdacontent n rdamedia nc rdacarrier Pitman research notes in mathematics series 360 Dirichlet, Problème de ram EDP inriac Laplace-vergelijking gtt Partiële differentiaalvergelijkingen gtt Sobolev ruimten gtt espace Sobolev inriac problème Dirichlet inriac équation Laplace inriac Dirichlet problem Dirichlet-Problem (DE-588)4129762-3 gnd rswk-swf Laplace-Differentialgleichung (DE-588)4228351-6 gnd rswk-swf Laplace-Differentialgleichung (DE-588)4228351-6 s Dirichlet-Problem (DE-588)4129762-3 s DE-604 Sohr, Hermann Verfasser (DE-588)106421379 aut Pitman research notes in mathematics series 360 (DE-604)BV000022845 360 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007500446&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Simader, Christian G. 1943-2019 Sohr, Hermann The Dirichlet problem for the Laplacian in bounded and unbounded domains a new approach to weak, strong and (2+k)-solutions in Sobolev-type spaces Pitman research notes in mathematics series Dirichlet, Problème de ram EDP inriac Laplace-vergelijking gtt Partiële differentiaalvergelijkingen gtt Sobolev ruimten gtt espace Sobolev inriac problème Dirichlet inriac équation Laplace inriac Dirichlet problem Dirichlet-Problem (DE-588)4129762-3 gnd Laplace-Differentialgleichung (DE-588)4228351-6 gnd |
| subject_GND | (DE-588)4129762-3 (DE-588)4228351-6 |
| title | The Dirichlet problem for the Laplacian in bounded and unbounded domains a new approach to weak, strong and (2+k)-solutions in Sobolev-type spaces |
| title_auth | The Dirichlet problem for the Laplacian in bounded and unbounded domains a new approach to weak, strong and (2+k)-solutions in Sobolev-type spaces |
| title_exact_search | The Dirichlet problem for the Laplacian in bounded and unbounded domains a new approach to weak, strong and (2+k)-solutions in Sobolev-type spaces |
| title_full | The Dirichlet problem for the Laplacian in bounded and unbounded domains a new approach to weak, strong and (2+k)-solutions in Sobolev-type spaces C. G. Simader and H. Sohr |
| title_fullStr | The Dirichlet problem for the Laplacian in bounded and unbounded domains a new approach to weak, strong and (2+k)-solutions in Sobolev-type spaces C. G. Simader and H. Sohr |
| title_full_unstemmed | The Dirichlet problem for the Laplacian in bounded and unbounded domains a new approach to weak, strong and (2+k)-solutions in Sobolev-type spaces C. G. Simader and H. Sohr |
| title_short | The Dirichlet problem for the Laplacian in bounded and unbounded domains |
| title_sort | the dirichlet problem for the laplacian in bounded and unbounded domains a new approach to weak strong and 2 k solutions in sobolev type spaces |
| title_sub | a new approach to weak, strong and (2+k)-solutions in Sobolev-type spaces |
| topic | Dirichlet, Problème de ram EDP inriac Laplace-vergelijking gtt Partiële differentiaalvergelijkingen gtt Sobolev ruimten gtt espace Sobolev inriac problème Dirichlet inriac équation Laplace inriac Dirichlet problem Dirichlet-Problem (DE-588)4129762-3 gnd Laplace-Differentialgleichung (DE-588)4228351-6 gnd |
| topic_facet | Dirichlet, Problème de EDP Laplace-vergelijking Partiële differentiaalvergelijkingen Sobolev ruimten espace Sobolev problème Dirichlet équation Laplace Dirichlet problem Dirichlet-Problem Laplace-Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007500446&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000022845 |
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