Methods for analysis of nonlinear elliptic boundary value problems:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English Russian |
| Published: |
Providence, RI
American Math. Soc.
1994
|
| Series: | Translations of mathematical monographs
139 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Aus dem Russ. übers. |
| Physical Description: | XI, 348 S. |
| ISBN: | 0821846167 |
Staff View
MARC
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| 240 | 1 | 0 | |a Metody issledovanija nelinejnych ėlliptičeskich graničnych zadač |
| 245 | 1 | 0 | |a Methods for analysis of nonlinear elliptic boundary value problems |c I. V. Skrypnik |
| 264 | 1 | |a Providence, RI |b American Math. Soc. |c 1994 | |
| 300 | |a XI, 348 S. | ||
| 336 | |b txt |2 rdacontent | ||
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| 490 | 1 | |a Translations of mathematical monographs |v 139 | |
| 500 | |a Aus dem Russ. übers. | ||
| 650 | 7 | |a Elliptische differentiaalvergelijkingen |2 gtt | |
| 650 | 7 | |a Equations différentielles elliptiques |2 ram | |
| 650 | 4 | |a Problèmes aux limites non linéaires | |
| 650 | 7 | |a Problèmes aux limites nonlinéaires |2 ram | |
| 650 | 7 | |a Randwaardeproblemen |2 gtt | |
| 650 | 4 | |a Équations différentielles elliptiques | |
| 650 | 4 | |a Differential equations, Elliptic | |
| 650 | 4 | |a Nonlinear boundary value problems | |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface ix
Chapter 1. Mappings of Monotone Type and Solvability of Quasilinear Bound¬
ary Value Problems 1
§ 1. Basic definitions and auxiliary propositions 1
§2. Reduction of problems for divergent equations to operator equations 5
§3. Formulation of variational problems and examples of nonlinear prob¬
lems in mechanics 10
§4. Solvability of coercive boundary value problems 14
§5. Solvability of equations with odd operators 18
§6. Other results on the solvability of nonlinear boundary value problems 21
Chapter 2. Degree of Generalized Monotone Mappings 31
§ 1. Degree of finite dimensional mappings 31
§2. Definition of degree of mappings of class a 35
§3. Degree of mappings in a nonseparable space 39
§4. Properties of the degree of generalized monotone mappings 42
§5. Computation of the index of a critical point 48
§6. Computation of the degree of potential mappings 54
§7. Application of the degree of a mapping to the solvability of operator
equations 57
§8. Additional remarks and results 64
Chapter 3. Topological Characteristics of Nonlinear Elliptic Boundary Value
Problems 69
§ 1. Preliminary information on the theory of linear elliptic problems 69
§2. Introduction of topological characteristics in the case of general nonlin¬
ear elliptic problems 73
§3. Coercive a priori estimates for pairs of linear elliptic operators 85
§4. Reduction of the Dirichlet problem for a general nonlinear elliptic equa¬
tion to an operator equation 95
Chapter 4. Solvability and Behavior of Solutions of Nonlinear Elliptic Bound¬
ary Value Problems 99
§ 1. Solvability of boundary value problems for divergent elliptic equations 99
§2. Solvability of general nonlinear boundary value problems 104
§3. Application of the index formula for a critical point 109
§4. Estimates of the number of solutions of nonlinear elliptic problems 118
§5. Strong convergence of Galerkin approximations for general nonlinear
elliptic boundary value problems 122
§6. Eigenvalues of nonlinear problems 124
vii
viii CONTENTS
§7. Further estimates of the number of solutions of nonlinear boundary
value problems 126
Chapter 5. Solvability of the Nonlinear Dirichlet Problem in a Narrow Strip 133
§ 1. Definitions and auxiliary inequalities 133
§2. Coercive estimates in W*mAA (Sh) for pairs of linear elliptic operators 142
§ 3. Estimates of solutions of the nonlinear Dirichlet problem 149
§4. Proof of the existence theorems 154
Chapter 6. Solvability of Semilinear Boundary Value Problems 159
§ 1. Perturbation of a uniquely solvable linear boundary value problem 159
§2. Perturbations of linear problems with nontrivial kernel 165
§3. Existence of multiple solutions of semilinear boundary value problems 173
Chapter 7. A Priori Estimates and Regularity of Solutions of Higher Order
Quasilinear Elliptic Equations 179
§1. Examples of irregular solutions 180
§2. Lp+S estimates of the rath order derivatives of generalized solutions 181
§3. A priori estimates of generalized (m + l)st order derivatives 191
§4. Conditions for the generalized solutions to belong to the space Cm¦ • 200
§5. Continuity of generalized solutions of higher order equations 205
§6. Partial regularity of generalized solutions of quasilinear elliptic equa¬
tions 212
§7. Interpolation methods in deriving a priori estimates 220
§8. Local energy estimates near the boundary and in the unbounded domain 228
Chapter 8. Behavior of Solutions of Quasilinear Elliptic Equations Near the
Boundary 233
§1. Auxiliary assertions 233
§2. A necessary condition of regularity of a boundary point 239
§3. A priori estimates for the auxiliary functions 245
§4. A sufficient condition of regularity of a boundary point 255
§5. A necessary condition of regularity of a boundary point (additional
results) 260
§6. Regularity of a boundary point for a higher order quasilinear elliptic
equation 261
Chapter 9. Nonlinear Elliptic Problems in Domains with Fine grained Bound¬
ary 265
§1. Formulation of conditions and results 266
§2. Estimates of solutions and of auxiliary functions 268
§3. Asymptotic expansion of the sequence of solutions 274
§4. Derivation of the limit equation 283
§5. Further results 292
Chapter 10. Homogenization of Nonlinear Dirichlet Problems in Domains
with Channels 297
§1. Formulation of assumptions and of main results 297
§2. Estimates of the solution of the model problem 303
§3. Asymptotic expansion of a sequence of solutions 324
§4. Proof of Theorem 1.1 335
References 343
|
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| ctrlnum | (OCoLC)30736067 (DE-599)BVBBV009938043 |
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| dewey-ones | 515 - Analysis |
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| dewey-search | 515/.35 |
| dewey-sort | 3515 235 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| id | DE-604.BV009938043 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:43:33Z |
| institution | BVB |
| isbn | 0821846167 |
| language | English Russian |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006583833 |
| oclc_num | 30736067 |
| open_access_boolean | |
| owner | DE-12 DE-11 DE-188 DE-634 |
| owner_facet | DE-12 DE-11 DE-188 DE-634 |
| physical | XI, 348 S. |
| publishDate | 1994 |
| publishDateSearch | 1994 |
| publishDateSort | 1994 |
| publisher | American Math. Soc. |
| record_format | marc |
| series | Translations of mathematical monographs |
| series2 | Translations of mathematical monographs |
| spelling | Skrypnik, Igorʹ Vladimirovič Verfasser aut Metody issledovanija nelinejnych ėlliptičeskich graničnych zadač Methods for analysis of nonlinear elliptic boundary value problems I. V. Skrypnik Providence, RI American Math. Soc. 1994 XI, 348 S. txt rdacontent n rdamedia nc rdacarrier Translations of mathematical monographs 139 Aus dem Russ. übers. Elliptische differentiaalvergelijkingen gtt Equations différentielles elliptiques ram Problèmes aux limites non linéaires Problèmes aux limites nonlinéaires ram Randwaardeproblemen gtt Équations différentielles elliptiques Differential equations, Elliptic Nonlinear boundary value problems Nichtlineares Randwertproblem (DE-588)4129830-5 gnd rswk-swf Elliptische Differentialgleichung (DE-588)4014485-9 gnd rswk-swf Elliptische Differentialgleichung (DE-588)4014485-9 s Nichtlineares Randwertproblem (DE-588)4129830-5 s DE-604 Translations of mathematical monographs 139 (DE-604)BV000002394 139 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006583833&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Skrypnik, Igorʹ Vladimirovič Methods for analysis of nonlinear elliptic boundary value problems Translations of mathematical monographs Elliptische differentiaalvergelijkingen gtt Equations différentielles elliptiques ram Problèmes aux limites non linéaires Problèmes aux limites nonlinéaires ram Randwaardeproblemen gtt Équations différentielles elliptiques Differential equations, Elliptic Nonlinear boundary value problems Nichtlineares Randwertproblem (DE-588)4129830-5 gnd Elliptische Differentialgleichung (DE-588)4014485-9 gnd |
| subject_GND | (DE-588)4129830-5 (DE-588)4014485-9 |
| title | Methods for analysis of nonlinear elliptic boundary value problems |
| title_alt | Metody issledovanija nelinejnych ėlliptičeskich graničnych zadač |
| title_auth | Methods for analysis of nonlinear elliptic boundary value problems |
| title_exact_search | Methods for analysis of nonlinear elliptic boundary value problems |
| title_full | Methods for analysis of nonlinear elliptic boundary value problems I. V. Skrypnik |
| title_fullStr | Methods for analysis of nonlinear elliptic boundary value problems I. V. Skrypnik |
| title_full_unstemmed | Methods for analysis of nonlinear elliptic boundary value problems I. V. Skrypnik |
| title_short | Methods for analysis of nonlinear elliptic boundary value problems |
| title_sort | methods for analysis of nonlinear elliptic boundary value problems |
| topic | Elliptische differentiaalvergelijkingen gtt Equations différentielles elliptiques ram Problèmes aux limites non linéaires Problèmes aux limites nonlinéaires ram Randwaardeproblemen gtt Équations différentielles elliptiques Differential equations, Elliptic Nonlinear boundary value problems Nichtlineares Randwertproblem (DE-588)4129830-5 gnd Elliptische Differentialgleichung (DE-588)4014485-9 gnd |
| topic_facet | Elliptische differentiaalvergelijkingen Equations différentielles elliptiques Problèmes aux limites non linéaires Problèmes aux limites nonlinéaires Randwaardeproblemen Équations différentielles elliptiques Differential equations, Elliptic Nonlinear boundary value problems Nichtlineares Randwertproblem Elliptische Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006583833&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000002394 |
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