Variational methods: applications to nonlinear partial differential equations and Hamiltonian systems
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2008
|
| Edition: | 4. ed. |
| Series: | Ergebnisse der Mathematik und ihrer Grenzgebiete / 3
34 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XX, 302 S. graph. Darst. |
| ISBN: | 9783540740124 9783540740131 |
Staff View
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Record in the Search Index
| _version_ | 1804137741807517696 |
|---|---|
| adam_text | MICHAEL STRUWE VARIATIONAL METHODS APPLICATIONS TO NONLINEAR PARTIAL
DIFFERENTIAL EQUATIONS AND HAMILTONIAN SYSTEMS FOURTH EDITION ^J
SPRINGER CONTENTS CHAPTER I. THE DIRECT METHODS IN THE CALCULUS OF
VARIATIONS 1 1. LOWER SEMI-CONTINUITY 2 DEGENERATE ELLIPTIC EQUATIONS, 4
* MINIMAL PARTITIONING HYPERSURFACES, 6 * MINIMAL HYPERSURFACES IN
RIEMANNIAN MANIFOLDS, 7 * A GENERAL LOWER SEMI-CONTINUITY RESULT, 8 2.
CONSTRAINTS 13 SEMILINEAR ELLIPTIC BOUNDARY VALUE PROBLEMS, 14 *
PERRON S METHOD IN A VARIATIONAL GUISE, 16 * THE CLASSICAL PLATEAU
PROBLEM, 19 3. COMPENSATED COMPACTNESS 25 APPLICATIONS IN ELASTICITY, 29
* CONVERGENCE RESULTS FOR NONLINEAR ELLIPTIC EQUATIONS, 32 * HARDY SPACE
METHODS, 35 4. THE CONCENTRATION-COMPACTNESS PRINCIPLE 36 EXISTENCE OF
EXTREMAL FUNCTIONS FOR SOBOLEV EMBEDDINGS, 42 5. EKELAND S VARIATIONAL
PRINCIPLE 51 EXISTENCE OF MINIMIZERS FOR QUASI-CONVEX FUNCTIONALS, 54 6.
DUALITY 58 HAMILTONIAN SYSTEMS, 60 * PERIODIC SOLUTIONS OF NONLINEAR
WAVE EQUATIONS, 65 7. MINIMIZATION PROBLEMS DEPENDING ON PARAMETERS 69
HARMONIC MAPS WITH SINGULARITIES, 71 CHAPTER II. MINIMAX METHODS 74 1.
THE FINITE DIMENSIONAL CASE 74 2. THE PALAIS-SMALE CONDITION 77 3. A
GENERAL DEFORMATION LEMMA 81 PSEUDO-GRADIENT FLOWS ON BANACH SPACES, 81
* PSEUDO-GRADIENT FLOWS ON MANIFOLDS, 85 4. THE MINIMAX PRINCIPLE 87
CLOSED GEODESIES ON SPHERES, 89 XVI CONTENTS 5. INDEX THEORY 94
KRASNOSELSKII GENUS, 94 * MINIMAX PRINCIPLES FOR EVEN FUNCTIONAL, 96 *
APPLICATIONS TO SEMILINEAR ELLIPTIC PROBLEMS, 98 * GENERAL INDEX
THEORIES, 99 * LJUSTERNIK-SCHNIRELMAN CATEGORY, 100 * A GEOMETRICAL
SMNDEX, 101 * MULTIPLE PERIODIC ORBITS OF HAMILTONIAN SYSTEMS, 103 6.
THE MOUNTAIN PASS LEMMA AND ITS VARIANTS 108 APPLICATIONS TO SEMILINEAR
ELLIPTIC BOUNDARY VALUE PROBLEMS, 110 * THE SYMMETRIC MOUNTAIN PASS
LEMMA, 112 * APPLICATION TO SEMILINEAR EQUA- TIONS WITH SYMMETRY, 116 7.
PERTURBATION THEORY 118 APPLICATIONS TO SEMILINEAR ELLIPTIC EQUATIONS,
120 8. LINKING 125 APPLICATIONS TO SEMILINEAR ELLIPTIC EQUATIONS, 128 *
APPLICATIONS TO HAMIL- TONIAN SYSTEMS, 130 9. PARAMETER DEPENDENCE 137
10. CRITICAL POINTS OF MOUNTAIN PASS TYPE 143 MULTIPLE SOLUTIONS OF
COERCIVE ELLIPTIC PROBLEMS, 147 11. NON-DIFFERENTIABLE PUNCTIONALS 150
12. LJUSTERNIK-SCHNIRELMAN THEORY ON CONVEX SETS 162 APPLICATIONS TO
SEMILINEAR ELLIPTIC BOUNDARY VALUE PROBLEMS, 166 CHAPTER III. LIMIT
CASES OF THE PALAIS-SMALE CONDITION 169 1. POHOZAEV S NON-EXISTENCE
RESULT 170 2. THE BREZIS-NIRENBERG RESULT 173 CONSTRAINED MINIMIZATION,
174 * THE UNCONSTRAINED CASE: LOCAL COMPACT- NESS, 175 * MULTIPLE
SOLUTIONS, 180 3. THE EFFECT OF TOPOLOGY 183 A GLOBAL COMPACTNESS
RESULT, 184 * POSITIVE SOLUTIONS ON ANNULAR-SHAPED REGIONS, 190 4. THE
YAMABE PROBLEM 194 THE VARIATIONAL APPROACH, 195 * THE LOCALLY
CONFORMALLY FLAT CASE, 197 * THE YAMABE FLOW, 198 * THE PROOF OF THEOREM
4.9 (FOLLOWING YE [1]), 200 * CONVERGENCE OF THE YAMABE FLOW IN THE
GENERAL CASE, 204 * THE COMPACT CASE UOO 0, 211 * BUBBLING: THE CASE
* = 0, 216 CONTENTS XVII 5. THE DIRICHLET PROBLEM FOR THE EQUATION OF
CONSTANT MEAN CURVATURE 220 SMALL SOLUTIONS, 221 * THE VOLUME
FUNCTIONAL, 223 * WENTE S UNIQUENESS RESULT, 225 * LOCAL COMPACTNESS,
226 * LARGE SOLUTIONS, 229 6. HARMONIC MAPS OF RIEMANNIAN SURFACES 231
THE EULER-LAGRANGE EQUATIONS FOR HARMONIC MAPS, 232 * BOCHNER IDENTITY,
234 * THE HOMOTOPY PROBLEM AND ITS FUNCTIONAL ANALYTIC SETTING, 234 *
EXISTENCE AND NON-EXISTENCE RESULTS, 237 * THE HEAT FLOW FOR HARMONIC
MAPS, 238 * THE GLOBAL EXISTENCE RESULT, 239 * THE PROOF OF THEOREM 6.6,
242 * FINITE-TIME BLOW-UP, 253 * REVERSE BUBBLING AND NONUNIQUENESS, 257
APPENDIX A 263 SOBOLEV SPACES, 263 * HOLDER SPACES, 264 * IMBEDDING
THEOREMS, 264 * DENSITY THEOREM, 265 * TRACE AND EXTENSION THEOREMS, 265
* POINCARE INEQUALITY, 266 APPENDIX B 268 SCHAUDER ESTIMATES, 268 *
-THEORY, 268 * WEAK SOLUTIONS, 269 * A REG- ULARITY RESULT, 269 *
MAXIMUM PRINCIPLE, 271 * WEAK MAXIMUM PRINCIPLE, 272 * APPLICATION, 273
APPENDIX C 274 FRECHET DIFFERENTIABILITY, 274 * NATURAL GROWTH
CONDITIONS, 276 REFERENCES 277 INDEX 301
|
| adam_txt |
MICHAEL STRUWE VARIATIONAL METHODS APPLICATIONS TO NONLINEAR PARTIAL
DIFFERENTIAL EQUATIONS AND HAMILTONIAN SYSTEMS FOURTH EDITION ^J
SPRINGER CONTENTS CHAPTER I. THE DIRECT METHODS IN THE CALCULUS OF
VARIATIONS 1 1. LOWER SEMI-CONTINUITY 2 DEGENERATE ELLIPTIC EQUATIONS, 4
* MINIMAL PARTITIONING HYPERSURFACES, 6 * MINIMAL HYPERSURFACES IN
RIEMANNIAN MANIFOLDS, 7 * A GENERAL LOWER SEMI-CONTINUITY RESULT, 8 2.
CONSTRAINTS 13 SEMILINEAR ELLIPTIC BOUNDARY VALUE PROBLEMS, 14 *
PERRON'S METHOD IN A VARIATIONAL GUISE, 16 * THE CLASSICAL PLATEAU
PROBLEM, 19 3. COMPENSATED COMPACTNESS 25 APPLICATIONS IN ELASTICITY, 29
* CONVERGENCE RESULTS FOR NONLINEAR ELLIPTIC EQUATIONS, 32 * HARDY SPACE
METHODS, 35 4. THE CONCENTRATION-COMPACTNESS PRINCIPLE 36 EXISTENCE OF
EXTREMAL FUNCTIONS FOR SOBOLEV EMBEDDINGS, 42 5. EKELAND'S VARIATIONAL
PRINCIPLE 51 EXISTENCE OF MINIMIZERS FOR QUASI-CONVEX FUNCTIONALS, 54 6.
DUALITY 58 HAMILTONIAN SYSTEMS, 60 * PERIODIC SOLUTIONS OF NONLINEAR
WAVE EQUATIONS, 65 7. MINIMIZATION PROBLEMS DEPENDING ON PARAMETERS 69
HARMONIC MAPS WITH SINGULARITIES, 71 CHAPTER II. MINIMAX METHODS 74 1.
THE FINITE DIMENSIONAL CASE 74 2. THE PALAIS-SMALE CONDITION 77 3. A
GENERAL DEFORMATION LEMMA 81 PSEUDO-GRADIENT FLOWS ON BANACH SPACES, 81
* PSEUDO-GRADIENT FLOWS ON MANIFOLDS, 85 4. THE MINIMAX PRINCIPLE 87
CLOSED GEODESIES ON SPHERES, 89 XVI CONTENTS 5. INDEX THEORY 94
KRASNOSELSKII GENUS, 94 * MINIMAX PRINCIPLES FOR EVEN FUNCTIONAL, 96 *
APPLICATIONS TO SEMILINEAR ELLIPTIC PROBLEMS, 98 * GENERAL INDEX
THEORIES, 99 * LJUSTERNIK-SCHNIRELMAN CATEGORY, 100 * A GEOMETRICAL
SMNDEX, 101 * MULTIPLE PERIODIC ORBITS OF HAMILTONIAN SYSTEMS, 103 6.
THE MOUNTAIN PASS LEMMA AND ITS VARIANTS 108 APPLICATIONS TO SEMILINEAR
ELLIPTIC BOUNDARY VALUE PROBLEMS, 110 * THE SYMMETRIC MOUNTAIN PASS
LEMMA, 112 * APPLICATION TO SEMILINEAR EQUA- TIONS WITH SYMMETRY, 116 7.
PERTURBATION THEORY 118 APPLICATIONS TO SEMILINEAR ELLIPTIC EQUATIONS,
120 8. LINKING 125 APPLICATIONS TO SEMILINEAR ELLIPTIC EQUATIONS, 128 *
APPLICATIONS TO HAMIL- TONIAN SYSTEMS, 130 9. PARAMETER DEPENDENCE 137
10. CRITICAL POINTS OF MOUNTAIN PASS TYPE 143 MULTIPLE SOLUTIONS OF
COERCIVE ELLIPTIC PROBLEMS, 147 11. NON-DIFFERENTIABLE PUNCTIONALS 150
12. LJUSTERNIK-SCHNIRELMAN THEORY ON CONVEX SETS 162 APPLICATIONS TO
SEMILINEAR ELLIPTIC BOUNDARY VALUE PROBLEMS, 166 CHAPTER III. LIMIT
CASES OF THE PALAIS-SMALE CONDITION 169 1. POHOZAEV'S NON-EXISTENCE
RESULT 170 2. THE BREZIS-NIRENBERG RESULT 173 CONSTRAINED MINIMIZATION,
174 * THE UNCONSTRAINED CASE: LOCAL COMPACT- NESS, 175 * MULTIPLE
SOLUTIONS, 180 3. THE EFFECT OF TOPOLOGY 183 A GLOBAL COMPACTNESS
RESULT, 184 * POSITIVE SOLUTIONS ON ANNULAR-SHAPED REGIONS, 190 4. THE
YAMABE PROBLEM 194 THE VARIATIONAL APPROACH, 195 * THE LOCALLY
CONFORMALLY FLAT CASE, 197 * THE YAMABE FLOW, 198 * THE PROOF OF THEOREM
4.9 (FOLLOWING YE [1]), 200 * CONVERGENCE OF THE YAMABE FLOW IN THE
GENERAL CASE, 204 * THE COMPACT CASE UOO 0, 211 * BUBBLING: THE CASE
* = 0, 216 CONTENTS XVII 5. THE DIRICHLET PROBLEM FOR THE EQUATION OF
CONSTANT MEAN CURVATURE 220 SMALL SOLUTIONS, 221 * THE VOLUME
FUNCTIONAL, 223 * WENTE'S UNIQUENESS RESULT, 225 * LOCAL COMPACTNESS,
226 * LARGE SOLUTIONS, 229 6. HARMONIC MAPS OF RIEMANNIAN SURFACES 231
THE EULER-LAGRANGE EQUATIONS FOR HARMONIC MAPS, 232 * BOCHNER IDENTITY,
234 * THE HOMOTOPY PROBLEM AND ITS FUNCTIONAL ANALYTIC SETTING, 234 *
EXISTENCE AND NON-EXISTENCE RESULTS, 237 * THE HEAT FLOW FOR HARMONIC
MAPS, 238 * THE GLOBAL EXISTENCE RESULT, 239 * THE PROOF OF THEOREM 6.6,
242 * FINITE-TIME BLOW-UP, 253 * REVERSE BUBBLING AND NONUNIQUENESS, 257
APPENDIX A 263 SOBOLEV SPACES, 263 * HOLDER SPACES, 264 * IMBEDDING
THEOREMS, 264 * DENSITY THEOREM, 265 * TRACE AND EXTENSION THEOREMS, 265
* POINCARE INEQUALITY, 266 APPENDIX B 268 SCHAUDER ESTIMATES, 268 *
"-THEORY, 268 * WEAK SOLUTIONS, 269 * A REG- ULARITY RESULT, 269 *
MAXIMUM PRINCIPLE, 271 * WEAK MAXIMUM PRINCIPLE, 272 * APPLICATION, 273
APPENDIX C 274 FRECHET DIFFERENTIABILITY, 274 * NATURAL GROWTH
CONDITIONS, 276 REFERENCES 277 INDEX 301 |
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| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| edition | 4. ed. |
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| id | DE-604.BV023373183 |
| illustrated | Illustrated |
| index_date | 2024-07-02T21:13:21Z |
| indexdate | 2024-07-09T21:17:07Z |
| institution | BVB |
| isbn | 9783540740124 9783540740131 |
| language | English |
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| physical | XX, 302 S. graph. Darst. |
| publishDate | 2008 |
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| publisher | Springer |
| record_format | marc |
| series2 | Ergebnisse der Mathematik und ihrer Grenzgebiete / 3 |
| spelling | Struwe, Michael 1955- Verfasser (DE-588)121295990 aut Variational methods applications to nonlinear partial differential equations and Hamiltonian systems Michael Struwe 4. ed. Berlin [u.a.] Springer 2008 XX, 302 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Ergebnisse der Mathematik und ihrer Grenzgebiete / 3 34 Calculus of variations Differential equations, Nonlinear Hamiltonian systems Nichtlineare Differentialgleichung (DE-588)4205536-2 gnd rswk-swf Variationsrechnung (DE-588)4062355-5 gnd rswk-swf Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 gnd rswk-swf Hamiltonsches System (DE-588)4139943-2 gnd rswk-swf Variationsrechnung (DE-588)4062355-5 s Nichtlineare Differentialgleichung (DE-588)4205536-2 s DE-604 Hamiltonsches System (DE-588)4139943-2 s Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 s 1\p DE-604 3 Ergebnisse der Mathematik und ihrer Grenzgebiete 34 (DE-604)BV000899194 34 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016556409&sequence=000001&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 | Struwe, Michael 1955- Variational methods applications to nonlinear partial differential equations and Hamiltonian systems Calculus of variations Differential equations, Nonlinear Hamiltonian systems Nichtlineare Differentialgleichung (DE-588)4205536-2 gnd Variationsrechnung (DE-588)4062355-5 gnd Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 gnd Hamiltonsches System (DE-588)4139943-2 gnd |
| subject_GND | (DE-588)4205536-2 (DE-588)4062355-5 (DE-588)4128900-6 (DE-588)4139943-2 |
| title | Variational methods applications to nonlinear partial differential equations and Hamiltonian systems |
| title_auth | Variational methods applications to nonlinear partial differential equations and Hamiltonian systems |
| title_exact_search | Variational methods applications to nonlinear partial differential equations and Hamiltonian systems |
| title_exact_search_txtP | Variational methods applications to nonlinear partial differential equations and Hamiltonian systems |
| title_full | Variational methods applications to nonlinear partial differential equations and Hamiltonian systems Michael Struwe |
| title_fullStr | Variational methods applications to nonlinear partial differential equations and Hamiltonian systems Michael Struwe |
| title_full_unstemmed | Variational methods applications to nonlinear partial differential equations and Hamiltonian systems Michael Struwe |
| title_short | Variational methods |
| title_sort | variational methods applications to nonlinear partial differential equations and hamiltonian systems |
| title_sub | applications to nonlinear partial differential equations and Hamiltonian systems |
| topic | Calculus of variations Differential equations, Nonlinear Hamiltonian systems Nichtlineare Differentialgleichung (DE-588)4205536-2 gnd Variationsrechnung (DE-588)4062355-5 gnd Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 gnd Hamiltonsches System (DE-588)4139943-2 gnd |
| topic_facet | Calculus of variations Differential equations, Nonlinear Hamiltonian systems Nichtlineare Differentialgleichung Variationsrechnung Nichtlineare partielle Differentialgleichung Hamiltonsches System |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016556409&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000899194 |
| work_keys_str_mv | AT struwemichael variationalmethodsapplicationstononlinearpartialdifferentialequationsandhamiltoniansystems |