Variational methods: applications to nonlinear partial differential equations and Hamiltonian systems
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
1996
|
| Edition: | 2., rev. and substantially expanded ed. |
| Series: | Ergebnisse der Mathematik und ihrer Grenzgebiete
3. Folge ; 34 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVI, 272 S. graph. Darst. |
| ISBN: | 3540588590 |
Staff View
MARC
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| 100 | 1 | |a Struwe, Michael |d 1955- |e Verfasser |0 (DE-588)121295990 |4 aut | |
| 245 | 1 | 0 | |a Variational methods |b applications to nonlinear partial differential equations and Hamiltonian systems |c Michael Struwe |
| 250 | |a 2., rev. and substantially expanded ed. | ||
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1996 | |
| 300 | |a XVI, 272 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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| 650 | 4 | |a Systèmes hamiltoniens | |
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Record in the Search Index
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| adam_text | 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 Genera! Lower
Semi-Continuity Result, 8
2. Constraints 13
Semi-Linear 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 57
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
xii Contents
5. Index Theory 94
Krasnoselskii Genus, 94 — Minimax Principles for Even Functionals, 96 —
Applications to Semilinear Elliptic Problems, 98 — General Index Theories,
99 — Ljusternik-Schnirelman Category, 100 — A Geometrical S1-Index, 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 Equations
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 Functionals 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 193
5. The Dirichlet Problem for the Equation of Constant Mean Curvature 203
Small Solutions, 204 — The Volume Functional, 206 — Wente s Uniqueness
Result, 208 — Local Compactness, 209 — Large Solutions, 212
Contents xiii
6. Harmonic Maps of Riemannian Surfaces 214
The Euler-Lagrange Equations for Harmonic Maps, 215 — Bochner identity,
217 — The Homotopy Problem and its Functional Analytic Setting, 217 —
Existence and Non-Existence Results, 220 — The Evolution of Harmonic
Maps, 221
Appendix A 237
Sobolev Spaces, 237 — Holder Spaces, 238 — Imbedding Theorems, 238 —
Density Theorem, 239 — Trace and Extension Theorems, 239 — Poincare
Inequality, 240
Appendix B 242
Schauder Estimates, 242 — L^-Theory, 242 — Weak Solutions, 243 — A Reg¬
ularity Result, 243 — Maximum Principle, 245 — Weak Maximum Principle,
246 — Application, 247
Appendix C 248
Frechet Differentiability, 248 — Natural Growth Conditions, 250
References 251
Index 271
|
| any_adam_object | 1 |
| author | Struwe, Michael 1955- |
| author_GND | (DE-588)121295990 |
| author_facet | Struwe, Michael 1955- |
| author_role | aut |
| author_sort | Struwe, Michael 1955- |
| author_variant | m s ms |
| building | Verbundindex |
| bvnumber | BV010755529 |
| callnumber-first | Q - Science |
| callnumber-label | QA316 |
| callnumber-raw | QA316 |
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| callnumber-sort | QA 3316 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 540 SK 660 |
| ctrlnum | (OCoLC)34564912 (DE-599)BVBBV010755529 |
| dewey-full | 515/.64 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.64 |
| dewey-search | 515/.64 |
| dewey-sort | 3515 264 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2., rev. and substantially expanded ed. |
| format | Book |
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| id | DE-604.BV010755529 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:58:21Z |
| institution | BVB |
| isbn | 3540588590 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007183568 |
| oclc_num | 34564912 |
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| physical | XVI, 272 S. graph. Darst. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | Springer |
| record_format | marc |
| series | Ergebnisse der Mathematik und ihrer Grenzgebiete |
| series2 | Ergebnisse der Mathematik und ihrer Grenzgebiete : 3. Folge |
| spelling | Struwe, Michael 1955- Verfasser (DE-588)121295990 aut Variational methods applications to nonlinear partial differential equations and Hamiltonian systems Michael Struwe 2., rev. and substantially expanded ed. Berlin [u.a.] Springer 1996 XVI, 272 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Ergebnisse der Mathematik und ihrer Grenzgebiete : 3. Folge 34 Calcul des variations Calcul des variations ram Dynamische systemen gtt Equations différentielles non linéaires ram Hamilton-vergelijkingen gtt Niet-lineaire vergelijkingen gtt Partiële differentiaalvergelijkingen gtt Systèmes hamiltoniens Systèmes hamiltoniens ram Variatieproblemen gtt Équations différentielles non linéaires Calculus of variations Differential equations, Nonlinear Hamiltonian systems Variationsrechnung (DE-588)4062355-5 gnd rswk-swf Hamiltonsches System (DE-588)4139943-2 gnd rswk-swf Nichtlineare Differentialgleichung (DE-588)4205536-2 gnd rswk-swf Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 gnd rswk-swf Hamiltonsches System (DE-588)4139943-2 s Variationsrechnung (DE-588)4062355-5 s DE-604 Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 s Nichtlineare Differentialgleichung (DE-588)4205536-2 s Ergebnisse der Mathematik und ihrer Grenzgebiete 3. Folge ; 34 (DE-604)BV000899194 34 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007183568&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Struwe, Michael 1955- Variational methods applications to nonlinear partial differential equations and Hamiltonian systems Ergebnisse der Mathematik und ihrer Grenzgebiete Calcul des variations Calcul des variations ram Dynamische systemen gtt Equations différentielles non linéaires ram Hamilton-vergelijkingen gtt Niet-lineaire vergelijkingen gtt Partiële differentiaalvergelijkingen gtt Systèmes hamiltoniens Systèmes hamiltoniens ram Variatieproblemen gtt Équations différentielles non linéaires Calculus of variations Differential equations, Nonlinear Hamiltonian systems Variationsrechnung (DE-588)4062355-5 gnd Hamiltonsches System (DE-588)4139943-2 gnd Nichtlineare Differentialgleichung (DE-588)4205536-2 gnd Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 gnd |
| subject_GND | (DE-588)4062355-5 (DE-588)4139943-2 (DE-588)4205536-2 (DE-588)4128900-6 |
| 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_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 | Calcul des variations Calcul des variations ram Dynamische systemen gtt Equations différentielles non linéaires ram Hamilton-vergelijkingen gtt Niet-lineaire vergelijkingen gtt Partiële differentiaalvergelijkingen gtt Systèmes hamiltoniens Systèmes hamiltoniens ram Variatieproblemen gtt Équations différentielles non linéaires Calculus of variations Differential equations, Nonlinear Hamiltonian systems Variationsrechnung (DE-588)4062355-5 gnd Hamiltonsches System (DE-588)4139943-2 gnd Nichtlineare Differentialgleichung (DE-588)4205536-2 gnd Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 gnd |
| topic_facet | Calcul des variations Dynamische systemen Equations différentielles non linéaires Hamilton-vergelijkingen Niet-lineaire vergelijkingen Partiële differentiaalvergelijkingen Systèmes hamiltoniens Variatieproblemen Équations différentielles non linéaires Calculus of variations Differential equations, Nonlinear Hamiltonian systems Variationsrechnung Hamiltonsches System Nichtlineare Differentialgleichung Nichtlineare partielle Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007183568&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000899194 |
| work_keys_str_mv | AT struwemichael variationalmethodsapplicationstononlinearpartialdifferentialequationsandhamiltoniansystems |