Partial differential operators of elliptic type:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English Japanese |
| Published: |
Providence, RI
American Math. Soc.
1992
|
| Series: | Translations of mathematical monographs
99 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Aus d. Japan. übers. |
| Physical Description: | XIII, 288 S. |
| ISBN: | 082184556X |
Staff View
MARC
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| 240 | 1 | 0 | |a Daenkei-henbibun-sayōso |
| 245 | 1 | 0 | |a Partial differential operators of elliptic type |c Norio Shimakura |
| 264 | 1 | |a Providence, RI |b American Math. Soc. |c 1992 | |
| 300 | |a XIII, 288 S. | ||
| 336 | |b txt |2 rdacontent | ||
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| 490 | 1 | |a Translations of mathematical monographs |v 99 | |
| 500 | |a Aus d. Japan. übers. | ||
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Record in the Search Index
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| adam_text | Contents
Preface to the Japanese Edition xi
Preface to the English Translation xiii
Chapter I. Partial Differential Operators of Elliptic Type 1
§1. Notation 1
§2. Defintions of elliptic operators 6
§3. Elementary solutions and parametrices 11
§4. Method of Levi 14
§5. Elliptic systems 17
Chapter II. The Laplacian in Euclidean Spaces 21
§ 1. Laplacian A and its elementary solutions 21
§2. Harmonic polynomials and Gegenbauer polynomials 27
§3. The polar coordinate system 30
§4. The Laplace Beltrami operator on the unit sphere 35
§5. Green functions in half spaces and rectangles 39
Chapter III. Constructions and Estimates of Elementary Solutions 45
§ 1. Elementary solutions of John 45
§2. Parametrices as pseudodifferential operators 50
§3. Estimates of parametrices (1) 56
§4. Estimates of parametrices (2) 59
§5. Elementary solutions of Hadamard 65
Chapter IV. Smoothness of Solutions 73
§1. Garding s inequality 73
§2. Interior Z,2 estimates and hypoellipticity 77
§3. Analytic hypoellipticity 80
§4. Interior Schauder estimates 84
§5. A theorem of de Giorgi, Nash, and Moser 91
Chapter V. Vishik Sobolev Problems 93
§1. Vishik Sobolev problems 93
§2. Smoothness of solutions 98
§3. Friedrichs extensions 102
vii
viii CONTENTS
§4. Green operators 104
§5. The Dirichlet problem for the Laplacian 107
§6. Asymptotic distribution of eigenvalues 111
Chapter VI. General Boundary Value Problems 119
§ 1. Method of continuity 119
§2. L a priori estimates 124
§3. Existence and uniqueness of solutions 132
§4. Green functions and Poisson kernels 140
§5. Indices and some comments 148
§6. General boundary value problems of Vishik Sobolev type 151
Chapter VII. Schauder Estimates and Applications 163
§ 1. Poisson kernels 163
§2. Schauder estimates 169
§3. Quasilinear elliptic equations (1) 172
§4. Quasilinear elliptic equations (2) 177
Chapter VIII. Degenerate Elliptic Operators 183
§1. Degenerate elliptic operators 183
§2. Weighted Sobolev spaces 189
§3. Models of ordinary differential operators (1) 195
§4. Models of ordinary differential operators (2) 201
§5. Dirichlet problem for second order equations 208
§6. General boundary value problems 211
§7. Supplements 214
§8. Examples of elementary solutions 217
Appendix 225
§A. Maximum principles 225
§B. Stokes formula and systems of boundary operators 228
§C. Preliminaries from ordinary differential equations 235
§D. Fredholm operators 243
§E. Sobolev spaces 246
§F. Holder spaces and Schauder spaces 260
§G. Geodesic distance 263
§H. Lemma for approximation of domains 268
§1. A priori estimates of Talenti 270
Bibliography 275
Subject Index 283
Notation 287
|
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| id | DE-604.BV005527998 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T16:31:07Z |
| institution | BVB |
| isbn | 082184556X |
| language | English Japanese |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-003464245 |
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| owner_facet | DE-384 DE-12 DE-355 DE-BY-UBR DE-824 DE-29T DE-19 DE-BY-UBM DE-634 DE-83 DE-11 DE-188 |
| physical | XIII, 288 S. |
| publishDate | 1992 |
| publishDateSearch | 1992 |
| publishDateSort | 1992 |
| publisher | American Math. Soc. |
| record_format | marc |
| series | Translations of mathematical monographs |
| series2 | Translations of mathematical monographs |
| spelling | Shimakura, Norio 1940- Verfasser (DE-588)172372771 aut Daenkei-henbibun-sayōso Partial differential operators of elliptic type Norio Shimakura Providence, RI American Math. Soc. 1992 XIII, 288 S. txt rdacontent n rdamedia nc rdacarrier Translations of mathematical monographs 99 Aus d. Japan. übers. Opérateurs hypoelliptiques Opérateurs hypoelliptiques ram Hypoelliptic operators Hypoelliptischer Operator (DE-588)4138891-4 gnd rswk-swf Elliptischer Differentialoperator (DE-588)4140057-4 gnd rswk-swf Elliptischer Differentialoperator (DE-588)4140057-4 s DE-604 Hypoelliptischer Operator (DE-588)4138891-4 s Translations of mathematical monographs 99 (DE-604)BV000002394 99 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003464245&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Shimakura, Norio 1940- Partial differential operators of elliptic type Translations of mathematical monographs Opérateurs hypoelliptiques Opérateurs hypoelliptiques ram Hypoelliptic operators Hypoelliptischer Operator (DE-588)4138891-4 gnd Elliptischer Differentialoperator (DE-588)4140057-4 gnd |
| subject_GND | (DE-588)4138891-4 (DE-588)4140057-4 |
| title | Partial differential operators of elliptic type |
| title_alt | Daenkei-henbibun-sayōso |
| title_auth | Partial differential operators of elliptic type |
| title_exact_search | Partial differential operators of elliptic type |
| title_full | Partial differential operators of elliptic type Norio Shimakura |
| title_fullStr | Partial differential operators of elliptic type Norio Shimakura |
| title_full_unstemmed | Partial differential operators of elliptic type Norio Shimakura |
| title_short | Partial differential operators of elliptic type |
| title_sort | partial differential operators of elliptic type |
| topic | Opérateurs hypoelliptiques Opérateurs hypoelliptiques ram Hypoelliptic operators Hypoelliptischer Operator (DE-588)4138891-4 gnd Elliptischer Differentialoperator (DE-588)4140057-4 gnd |
| topic_facet | Opérateurs hypoelliptiques Hypoelliptic operators Hypoelliptischer Operator Elliptischer Differentialoperator |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003464245&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000002394 |
| work_keys_str_mv | AT shimakuranorio daenkeihenbibunsayoso AT shimakuranorio partialdifferentialoperatorsofelliptictype |