Linear differential equations of principal type:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York u.a.
Consulatants Bureau
1986
|
| Series: | Contemporary Soviet mathematics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | EST: Linejnye differencial'nye uravnenija glavnogo tipa <engl.>. - Aus d. Russ. übers. |
| Physical Description: | VII, 301 S. |
| ISBN: | 0306109921 |
Staff View
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| 100 | 1 | |a Egorov, Jurij V. |d 1938- |e Verfasser |0 (DE-588)121177181 |4 aut | |
| 245 | 1 | 0 | |a Linear differential equations of principal type |c Yu. V. Egorov |
| 264 | 1 | |a New York u.a. |b Consulatants Bureau |c 1986 | |
| 300 | |a VII, 301 S. | ||
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| 490 | 0 | |a Contemporary Soviet mathematics | |
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Record in the Search Index
| _version_ | 1804115194988724224 |
|---|---|
| adam_text | CONTENTS
INTRODUCTION 1
CHAPTER I
Distribution Theory 9
§1. Definitions and basic properties of distributions 9
§2. Fourier transforms and convolution of distributions 16
5 3. Sobolev spaces 20
§4. Differential operators with constant coefficients 27
§5. Distributions on manifolds 36
CHAPTER II
Pseudo Differential Operators 43
§1. Singular integral operators 43
§2. Definitions and basic properties of pseudo differential
operators 46
§3. Elliptic pseudo differential operators 57
§4. Canonical transformations 66
§5. Garding s inequality 85
§6. Generalizations 90
§7. A class of pseudo differential operators 92
CHAPTER III
Boundary Problems for Elliptic Equations 97
51. Equations with constant coefficients in a half space 97
§2. Boundary problems for equations with variable coefficients 101
§3. Reduction of a boundary problem to a pseudo differential
equation 104
CHAPTER IV
The Oblique Derivative Problem 107
51. Statement of the problem. Examples 107
§2. Auxiliary constructions 109
§3. Manifolds of class I Ill
§4. Manifolds of class II 122
§5. Manifolds of class III 126
CHAPTER V
Wave Front Sets. Fourier Integral Operators 131
51. Wave front sets. Definition and examples 131
§2. Basic properties of a wave front set 133
§3. Another approach to the study of wave fronts 135
§4. Wave front sets and mappings 137
§5. Wave front set and Fourier integral operators 142
§6. Propagation of singularities. Solvability of equations of
principal type with a real valued principal symbol 146
v
vi CONTENTS
CHAPTER VI
Necessary Conditions for Local Solvability. 151
§1. Examples 151
§2. HBrmander s theorem , 152
§3. Finite order zero theorem 160
§4. Structure of the symbol 166
§5. Infinite order zero theorem 174
CHAPTER VII
Sufficient Conditions for Local Solvability. 183
§ 1. Review of results 183
§2. Reduction to first order operators 186
§3. Proof of Theorem 2.1 190
CHAPTER VIII
Subelliptic Operators 195
§1. Definitions and basic properties 195
§2. Localization of estimates 201
§3. Necessary conditions for subellipticity 204
§4. Estimates for differential operators of the first class 207
§5. Sufficient conditions for subellipticity 226
§6. Canonical transformations and partition of unity 246
§7. Applications to the oblique derivative problem 250
§8. Applications to the 3 Neumann problem 252
CHAPTER IX
The Cauchy Problem 259
51. Statement of the problem 259
§2. Kovalevsky theorem 260
§3. Hyperbolic equations 264
§4. Carleman estimates 270
§5. Calderon s theorem 272
COMMENTS 281
BIBLIOGRAPHY 285
|
| any_adam_object | 1 |
| author | Egorov, Jurij V. 1938- |
| author_GND | (DE-588)121177181 |
| author_facet | Egorov, Jurij V. 1938- |
| author_role | aut |
| author_sort | Egorov, Jurij V. 1938- |
| author_variant | j v e jv jve |
| building | Verbundindex |
| bvnumber | BV000742977 |
| classification_rvk | SK 540 SK 560 SK 620 |
| classification_tum | MAT 350f |
| ctrlnum | (OCoLC)246888668 (DE-599)BVBBV000742977 |
| dewey-full | 515.354 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.354 |
| dewey-search | 515.354 |
| dewey-sort | 3515.354 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV000742977 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:18:45Z |
| institution | BVB |
| isbn | 0306109921 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-000465094 |
| oclc_num | 246888668 |
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| owner | DE-12 DE-91G DE-BY-TUM DE-824 DE-706 DE-188 |
| owner_facet | DE-12 DE-91G DE-BY-TUM DE-824 DE-706 DE-188 |
| physical | VII, 301 S. |
| publishDate | 1986 |
| publishDateSearch | 1986 |
| publishDateSort | 1986 |
| publisher | Consulatants Bureau |
| record_format | marc |
| series2 | Contemporary Soviet mathematics |
| spelling | Egorov, Jurij V. 1938- Verfasser (DE-588)121177181 aut Linear differential equations of principal type Yu. V. Egorov New York u.a. Consulatants Bureau 1986 VII, 301 S. txt rdacontent n rdamedia nc rdacarrier Contemporary Soviet mathematics EST: Linejnye differencial'nye uravnenija glavnogo tipa <engl.>. - Aus d. Russ. übers. Lineare Differentialgleichung Lineare Differentialgleichung (DE-588)4206889-7 gnd rswk-swf Partielle Differentialgleichung (DE-588)4044779-0 gnd rswk-swf Lineare Differentialgleichung (DE-588)4206889-7 s DE-604 Partielle Differentialgleichung (DE-588)4044779-0 s 1\p DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000465094&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Egorov, Jurij V. 1938- Linear differential equations of principal type Lineare Differentialgleichung Lineare Differentialgleichung (DE-588)4206889-7 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd |
| subject_GND | (DE-588)4206889-7 (DE-588)4044779-0 |
| title | Linear differential equations of principal type |
| title_auth | Linear differential equations of principal type |
| title_exact_search | Linear differential equations of principal type |
| title_full | Linear differential equations of principal type Yu. V. Egorov |
| title_fullStr | Linear differential equations of principal type Yu. V. Egorov |
| title_full_unstemmed | Linear differential equations of principal type Yu. V. Egorov |
| title_short | Linear differential equations of principal type |
| title_sort | linear differential equations of principal type |
| topic | Lineare Differentialgleichung Lineare Differentialgleichung (DE-588)4206889-7 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd |
| topic_facet | Lineare Differentialgleichung Partielle Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000465094&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT egorovjurijv lineardifferentialequationsofprincipaltype |