Elliptic problems in domains with piecewise smooth boundaries:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin u.a.
de Gruyter
1994
|
| Series: | De Gruyter expositions in mathematics
13 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VII, 525 S. |
| ISBN: | 3110135221 |
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MARC
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| 100 | 1 | |a Nazarov, Sergej A. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Elliptic problems in domains with piecewise smooth boundaries |c by Sergey A. Nazarov ; Boris A. Plamenevsky |
| 264 | 1 | |a Berlin u.a. |b de Gruyter |c 1994 | |
| 300 | |a VII, 525 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a De Gruyter expositions in mathematics |v 13 | |
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Record in the Search Index
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| adam_text | Contents
Introduction 1
Chapter 1
Elliptic boundary value problems in domains with smooth boundary 4
§1. Elliptic boundary value problems 4
§ 2. Elliptic problems with a parameter 11
Chapter 2
Dirichlet and Neumann problems for the Laplace operator in
plane domains with corner points at the boundary 21
§ 1. Generalized solutions of the Dirichlet and Neumann problems in
domains with corner points. Deviations from the usual properties
of solutions 21
§ 2. Solvability and asymptotics of solutions of model problems in a strip
and in an angle 24
§ 3. The Dirichlet problem in a bounded domain with a corner point 31
§ 4. The Neumann problem in a bounded domain with a corner point 38
Chapter 3
General elliptic boundary value problems in a cylinder and in a cone 43
§ 1. Solvability and asymptotics of solutions of boundary value problems
in a cylinder with the coefficients constant along the axis 43
§ 2. Calculation of the coefficients cf J) in the asymptotics of the solution 49
§ 3. Asymptotics of the solutions of boundary value problems in a cylinder
with right hand side of a special form 53
§4. Solvability and asymptotics of solutions of the boundary value problems
with periodic coefficients 55
§ 5. Boundary value problems in a cone 63
§ 6. Estimates and asymptotics of solutions in Lp and Holder classes 74
§ 7. Fundamental solutions of the boundary value problem in a cone 82
§ 8. Two examples: The Dirichlet problem and the oblique derivative
problem 92
Chapter 4
General elliptic problems in domains with conical points 97
§ 1. The Fredholm property 97
§ 2. Asymptotics of solutions near conical points 105
vi Contents
§ 3. Expressions for the coefficients in asymptotic formulas. Properties of
the index 109
§4. Asymptotics of fundamental solutions 117
§5. Boundary value problems in spaces with nonhomogeneous norms 127
Chapter 5
Self adjoint problems in domains with outlets to infinity 144
§ 1. Self adjoint problems in domains with cylindrical outlets to infinity 144
§ 2. Special choices of Jordan chains of self adjoint operator pencils 148
§ 3. Waves, scattering matrices and intrinsic radiation conditions 156
§4. Energetic solutions and the polarization matrix 161
§ 5. The extensions of the symmetric operator . 175
§ 6. On a problem of the scattering of electro magnetic waves 181
§ 7. Elasticity problems in domains having cylindrical outlets to infinity 192
§ 8. Stokes and Navier Stokes problems in domains with cylindrical outlets
to infinity 214
Chapter 6
Self adjoint problems in domains with conical points. Applications 222
§ 1. Self adjoint problems. Properties of their pencils 222
§ 2. The generalized Green formula, radiation conditions 229
§ 3. Self adjoint extensions in spaces with weighted norms 236
§4. Boundary value problems in domains with compact complement.
The polarization matrix 241
§ 5. Asymptotic analysis of the problem in domains with small holes 248
§ 6. Two problems in plates theory 263
Chapter 7
Applications to crack theory 271
§ 1. Stress singularities at a crack tip 271
§ 2. The rupture criterion 279
§ 3. The Cherepanov Rice integral 286
§4. On the structure of the spectrum of the pencil generated by a
self adjoint problem in a plane domain with a crack 290
Chapter 8
Elliptic problems in domains with smooth edges 298
§ 1. Statement of the problem. Model problems 298
§ 2. Analysis of the model problems 302
§ 3. The Fredholm property of the elliptic problem in a bounded domain 308
§4. The Dirichlet and the Neumann problems for self adjoint systems 311
§5. Lp estimates of solutions 319
§ 6. Estimates of solutions in weighted Holder classes 326
Contents vii
Chapter 9
Elliptic problems on manifolds with intersecting edges 337
§1. Manifolds of the class D 337
§ 2. Differential operators on class X manifolds 344
§3. The function spaces 351
§4. Statement of the boundary problems. Model problems 354
§ 5. Boundary value problems on class D manifolds 360
§ 6. The Dirichlet and Neumann problems for self adjoint systems 363
Chapter 10
Asymptotics of solutions of the Dirichlet problem for the Laplace operator
in a three dimensional domain having edges on the boundary 384
§ 1. Asymptotics of solution near smooth edges 384
§ 2. Asymptotics of solutions near the singular point having the type of the
vertex of a polyhedron 388
§ 3. Formulas for coefficients in asymptotics of solutions near an edge 392
Chapter 11
The asymptotics of solutions of general problems near edges 396
§1. Guidelines for constructing asymptotics. Auxiliary assertions 397
§ 2. The asymptotics of solutions near an edge (in case of a smooth
right hand side) 404
§ 3. Asymptotics of solutions near an edge (general case) 410
§ 4. Corollaries of asymptotic formulas 430
Chapter 12
Self adjoint problems with radiation conditions on the edges 441
§ 1. Setting of boundary value problems and information about the
asymptotics of solutions 441
§ 2. The generalized Green formula. Fredholm property of the problem with
radiation conditions 444
§ 3. Solvability conditions for the problem with radiation conditions in terms
of the generalized Green formula 454
§ 4. Intrinsic radiation conditions on the edge 465
§ 5. Energetic radiation conditions. The polarization operator on the edge 477
§ 6. The scattering operator. The formula for the increment of the dimension
of the kernel of the operator of the problem generated by the variation of
the weight factor 485
§7. Sobolev problems 497
§ 8. The three dimensional problem of crack mechanics 504
Bibliographical notes 515
References 517
Index 523
List of spaces 525
|
| any_adam_object | 1 |
| author | Nazarov, Sergej A. Plamenevskij, Boris A. |
| author_facet | Nazarov, Sergej A. Plamenevskij, Boris A. |
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| institution | BVB |
| isbn | 3110135221 |
| language | English |
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| physical | VII, 525 S. |
| publishDate | 1994 |
| publishDateSearch | 1994 |
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| publisher | de Gruyter |
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| series | De Gruyter expositions in mathematics |
| series2 | De Gruyter expositions in mathematics |
| spelling | Nazarov, Sergej A. Verfasser aut Elliptic problems in domains with piecewise smooth boundaries by Sergey A. Nazarov ; Boris A. Plamenevsky Berlin u.a. de Gruyter 1994 VII, 525 S. txt rdacontent n rdamedia nc rdacarrier De Gruyter expositions in mathematics 13 Equations différentielles elliptiques ram Problèmes aux limites ram Boundary value problems Differential equations, Elliptic 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 Elliptisches Randwertproblem (DE-588)4193399-0 s DE-604 Elliptische Differentialgleichung (DE-588)4014485-9 s Randwertproblem (DE-588)4048395-2 s Plamenevskij, Boris A. Verfasser aut De Gruyter expositions in mathematics 13 (DE-604)BV004069300 13 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006352950&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Nazarov, Sergej A. Plamenevskij, Boris A. Elliptic problems in domains with piecewise smooth boundaries De Gruyter expositions in mathematics Equations différentielles elliptiques ram Problèmes aux limites ram Boundary value problems Differential equations, Elliptic 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 domains with piecewise smooth boundaries |
| title_auth | Elliptic problems in domains with piecewise smooth boundaries |
| title_exact_search | Elliptic problems in domains with piecewise smooth boundaries |
| title_full | Elliptic problems in domains with piecewise smooth boundaries by Sergey A. Nazarov ; Boris A. Plamenevsky |
| title_fullStr | Elliptic problems in domains with piecewise smooth boundaries by Sergey A. Nazarov ; Boris A. Plamenevsky |
| title_full_unstemmed | Elliptic problems in domains with piecewise smooth boundaries by Sergey A. Nazarov ; Boris A. Plamenevsky |
| title_short | Elliptic problems in domains with piecewise smooth boundaries |
| title_sort | elliptic problems in domains with piecewise smooth boundaries |
| topic | Equations différentielles elliptiques ram Problèmes aux limites ram Boundary value problems Differential equations, Elliptic Elliptisches Randwertproblem (DE-588)4193399-0 gnd Randwertproblem (DE-588)4048395-2 gnd Elliptische Differentialgleichung (DE-588)4014485-9 gnd |
| topic_facet | Equations différentielles elliptiques Problèmes aux limites Boundary value problems Differential equations, Elliptic Elliptisches Randwertproblem Randwertproblem Elliptische Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006352950&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV004069300 |
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