Elliptic boundary value problems in domains with point singularities:
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, Rhode Island
American Mathematical Society
[1997]
|
| Series: | Mathematical surveys and monographs
Volume 52 |
| Subjects: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008121562&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Physical Description: | ix, 414 Seiten |
| ISBN: | 0821807544 9780821807545 |
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MARC
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| 245 | 1 | 0 | |a Elliptic boundary value problems in domains with point singularities |c V. A. Kozlov ; V. G. Maz'ya ; J. Rossmann |
| 264 | 1 | |a Providence, Rhode Island |b American Mathematical Society |c [1997] | |
| 264 | 4 | |c © 1997 | |
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| 490 | 1 | |a Mathematical surveys and monographs |v Volume 52 | |
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| 700 | 1 | |a Roßmann, Jürgen |d 1954- |e Verfasser |0 (DE-588)122254856 |4 aut | |
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Record in the Search Index
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| adam_text |
Contents
Introduction 1
Part 1. Elliptic boundary value problems in domains with smooth
boundary 7
Chapter 1. Boundary value problems for ordinary differential equations on
the half axis 9
1.1. The boundary value problem and its formally adjoint 9
1.2. Solvability of the boundary value problem on the half axis 13
1.3. Solvability of regular problems on the half axis in Sobolev spaces of
negative order 20
1.4. Properties of the operator adjoint to the operator of the boundary
value problem 26
Chapter 2. Elliptic boundary value problems in the half space 31
2.1. Periodic solutions of partial differential equations 31
2.2. Solvability of elliptic boundary value problems in the half space 35
2.3. Solvability of elliptic boundary value problems in the half space in
Sobolev spaces of arbitrary integer order 43
Chapter 3. Elliptic boundary value problems in smooth domains 59
3.1. The boundary value problem and its formally adjoint 59
3.2. An a priori estimate for the solution 72
3.3. The adjoint operator 80
3.4. Solvability of elliptic boundary value problems in smooth domains 84
3.5. The Green function of the boundary value problem 90
3.6. Elliptic boundary value problems with parameter 98
Chapter 4. Variants and extensions 105
4.1. Elliptic problems with boundary operators of higher order in a smooth
bounded domain 105
4.2. Boundary value problems for elliptic systems of differential equations 111
4.3. Boundary value problems in the variational form 119
4.4. Further results 134
4.5. Notes 138
Part 2. Elliptic problems in domains with conical points 143
Chapter 5. Elliptic boundary value problems in an infinite cylinder 145
vii
viii contents
5.1. Operator valued polynomials and applications to ordinary differential
equations with operator coefficients 145
5.2. Solvability of the model problem in an infinite cylinder 153
5.3. Solvability of the model problem in the cylinder in Sobolev spaces of
negative order 161
5.4. Asymptotics of the solution of the model problem at infinity 168
5.5. The boundary value problem with coefficients which stabilize at infinity 180
Chapter 6. Elliptic boundary value problems in domains with conical points 191
6.1. The model problem in an infinite cone 191
6.2. Elliptic boundary value problems in a bounded domain with conical
points 212
6.3. Solvability of elliptic boundary value problems in bounded domains
with conical points 219
6.4. Asymptotics of the solution 234
6.5. Boundary value problems with parameter in domains with conical
points 246
6.6. Examples 260
Chapter 7. Elliptic boundary value problems in weighted Sobolev spaces with
nonhomogeneous norms 267
7.1. Relations between weighted Sobolev spaces 267
7.2. Elliptic problems in spaces with nonhomogeneous norms 277
7.3. Weighted Sobolev spaces with critical value of the weight parameter 286
Chapter 8. Variants and extensions 303
8.1. Elliptic problems with boundary operators of higher order in bounded
domains with conical points 303
8.2. Elliptic problems for systems of differential equations 309
8.3. Boundary value problems in the variational form 315
8.4. Further results 322
8.5. Notes 332
Part 3. Elliptic problems in domains with cuspidal points 335
Chapter 9. Elliptic boundary value problems in domains with exterior cusps 337
9.1. Elliptic boundary value problems in quasicylindrical domains 337
9.2. Elliptic boundary value problems in cuspidal domains 346
9.3. Variants and extensions 349
9.4. Further results 354
9.5. Notes 356
Chapter 10. Elliptic boundary value problems in domains with inside cusps 357
10.1. Formulation of the problem 358
10.2. The first limit problem 362
10.3. The second limit problem 369
10.4. The auxiliary problem 377
10.5. Elliptic problems in domains of the exterior of a cusp type 388
10.6. Notes 396
Bibliography 397
CONTENTS ix
Index 409
List of Symbols 413 |
| any_adam_object | 1 |
| author | Kozlov, Vladimir 1954- Mazʹja, Vladimir Gilelevič 1937- Roßmann, Jürgen 1954- |
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| author_sort | Kozlov, Vladimir 1954- |
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| bvnumber | BV012002289 |
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| ctrlnum | (OCoLC)246872941 (DE-599)BVBBV012002289 |
| discipline | Mathematik |
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| id | DE-604.BV012002289 |
| illustrated | Not Illustrated |
| indexdate | 2025-04-15T08:00:58Z |
| institution | BVB |
| isbn | 0821807544 9780821807545 |
| language | English |
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| oclc_num | 246872941 |
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| physical | ix, 414 Seiten |
| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | Mathematical surveys and monographs |
| series2 | Mathematical surveys and monographs |
| spelling | Kozlov, Vladimir 1954- Verfasser (DE-588)103679014 aut Elliptic boundary value problems in domains with point singularities V. A. Kozlov ; V. G. Maz'ya ; J. Rossmann Providence, Rhode Island American Mathematical Society [1997] © 1997 ix, 414 Seiten txt rdacontent n rdamedia nc rdacarrier Mathematical surveys and monographs Volume 52 Grenzwert <Mathematik> - Lineare elliptische Differentialgleichung Singularität Mathematik (DE-588)4077459-4 gnd rswk-swf Elliptisches Randwertproblem (DE-588)4193399-0 gnd rswk-swf Elliptisches Randwertproblem (DE-588)4193399-0 s Singularität Mathematik (DE-588)4077459-4 s DE-604 Mazʹja, Vladimir Gilelevič 1937- Verfasser (DE-588)121490602 aut Roßmann, Jürgen 1954- Verfasser (DE-588)122254856 aut Erscheint auch als Online-Ausgabe 978-0-8218-3377-3 Mathematical surveys and monographs Volume 52 (DE-604)BV000018014 52 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008121562&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kozlov, Vladimir 1954- Mazʹja, Vladimir Gilelevič 1937- Roßmann, Jürgen 1954- Elliptic boundary value problems in domains with point singularities Mathematical surveys and monographs Grenzwert <Mathematik> - Lineare elliptische Differentialgleichung Singularität Mathematik (DE-588)4077459-4 gnd Elliptisches Randwertproblem (DE-588)4193399-0 gnd |
| subject_GND | (DE-588)4077459-4 (DE-588)4193399-0 |
| title | Elliptic boundary value problems in domains with point singularities |
| title_auth | Elliptic boundary value problems in domains with point singularities |
| title_exact_search | Elliptic boundary value problems in domains with point singularities |
| title_full | Elliptic boundary value problems in domains with point singularities V. A. Kozlov ; V. G. Maz'ya ; J. Rossmann |
| title_fullStr | Elliptic boundary value problems in domains with point singularities V. A. Kozlov ; V. G. Maz'ya ; J. Rossmann |
| title_full_unstemmed | Elliptic boundary value problems in domains with point singularities V. A. Kozlov ; V. G. Maz'ya ; J. Rossmann |
| title_short | Elliptic boundary value problems in domains with point singularities |
| title_sort | elliptic boundary value problems in domains with point singularities |
| topic | Grenzwert <Mathematik> - Lineare elliptische Differentialgleichung Singularität Mathematik (DE-588)4077459-4 gnd Elliptisches Randwertproblem (DE-588)4193399-0 gnd |
| topic_facet | Grenzwert <Mathematik> - Lineare elliptische Differentialgleichung Singularität Mathematik Elliptisches Randwertproblem |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008121562&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000018014 |
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