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Struwe M., Rappoport M. — Variational Methods: Applications to Nonlinear Partial Differential Equations and Hamiltonian Systems
Struwe M., Rappoport M. — Variational Methods: Applications to Nonlinear Partial Differential Equations and Hamiltonian Systems

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Название: Variational Methods: Applications to Nonlinear Partial Differential Equations and Hamiltonian Systems

Авторы: Struwe M., Rappoport M.

Аннотация:

Hilbert's talk at the second International Congress of 1900 in Paris marked the beginning of a new era in the calculus of variations. A development began which, within a few decades, brought tremendous success, highlighted by the 1929 theorem of Ljusternik and Schnirelman on the existence of three distinct prime closed geodesics on any compact surface of genus zero, and the 1930/31 solution of Plateau's problem by Douglas and Radó. The book gives a concise introduction to variational methods and presents an overview of areas of current research in the field. The third edition gives a survey on new developments in the field. References have been updated and a small number of mistakes have been rectified.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2000

Количество страниц: 244

Добавлена в каталог: 18.08.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Approximate solutions      32
Area      6 19
Bifurcation      164 ff.
Burrier      54 221
Calderon — Zygmund inequality      216 f.
Caratheodory function      223
Category      92 see
Change in topology      154
Characteristic function      6
Co-area formula      41
Coercive functional      4
Coercive operator      56
Compactness, bounded compactness      2
Compactness, compensated compactness      25 ff.
Compactness, concentration-compactness      37 f. 42
Compactness, local compactness      39 160 169 186 191 see
Compactness, of a sequence of measures      37
Concentration-function (of measure)      38
Conformal, $\epsilon$-conformality theorem of Money      20
Conformal, conformal group of the disc      21
Conformal, conformal invariance      20 39 154
Conformal, conformality relation      20
Convexity polyconvex      25
Convexity quasiconvex      51
Critical point (value)      1
Critical point (value), at infinity      169
Critical point (value), in convex sets      148
Critical point (value), of mountain pass type      128
Critical point (value), of non-differentiable functional      137
Critical point (value), saddle point      1
Deformation Lemma      73 ff
Deformation lemma, for ${C}^{1}$-functionals on Banach spaces      75
Deformation lemma, for non-differentiable functionals      138 143 146
Deformation lemma, on convex sets      150
Deformation lemma, on manifolds      79
Dichotomy (of a sequence of measures)      38
Dirichlet integral      20
Dual variational problem      58
Eigenvalue for Dirichlet problem, Courant — Fischer characterization      89
Eigenvalue for Dirichlet problem, Rayleigh — Ritz characterization      14
Eigenvalue for Dirichlet problem, Weyl asymptotic formula      109
Elliptic equations      14 ff. 16 30 90 102 108 111 119 132 151
Elliptic equations, degenerate elliptic equations      4 168
Elliptic equations, on unbounded domains      34 ff.
Elliptic equations, with critical growth      155 ff.
Energy, energy functional      191
Energy, energy inequality      196 202
Energy, energy surface      57
Energy, stored energy      25
Epigraph      54
Equivariant      74
Euler — Lagrange equations      1
Finsler manifolds      77 f.
Frechet differential      222
Functional at infinity      34
Genus      see “Krasnoselskii genus”
Geodesics      58
Geodesics, closed geodesics on spheres      81 ff.
Gradient      76
Gradient, gradient-flow      76 126
Group action      74 76 78
Hamiltonian systems      57 ff. 95 121 135
Harmonic map      8 154 191
Harmonic map, evolution problem      196 197
Harmonic sphere      8 198
INDEX      86 91
Index, Bend-index      93 ff.
Index, Krasnoselskii genus      86 ff.
Index, Ljusternik — Schnirelman category      92 f.
Index, pseudo-index      93
Intersection lemma      105
Invariant under flow      79
Invariant under group action      see “Equivariant”
Isoperimetric inequality      41 184
Legendre condition      13
Legendre — Fenchel transform      55 f. 60
Limiting problem      155 169
Linking      116 f.
Linking, examples of linking sets      116 ff. 125
Lower semi-continuity      3 8 51
Maximum principle      42 219
Mean curvature equation      154 180
Measure, compactness of a sequence of measures      37
Measure, concentration function of measure      38
Measure, dichotomy of a sequence of measures      38
Measure, vanishing of a sequence of measures      37
Minimal surface      5 f. 7 19 154
Minimal surface, minimal cones      6
Minimal surface, minimal partitioning surfaces      5 f.
Minimal surface, parametric minimal surface      20
Minimax principle      79 ff. 88
Minimax principle, Courant — Fischer      89
Minimax principle, Palais      79
Minimizer      1 129 150
Minimizing sequence      3 51
Monotone operator      56
Monotonicity (of index)      87
Mountain pass lemma      66 68 101 104
Palais — Smale condition      69 ff.
Palais — Smale condition, (C)      70
Palais — Smale condition, (P.-S.)      70
Palais — Smale condition, Cerami's variant      72
Palais — Smale condition, for non-differentiable functionals      137
Palais — Smale condition, local      162
Palais — Smale condition, on convex sets      148
Palais — Smale sequence      50 70
Perimeter (of a set)      6
Periodic solutions, of Hamiltonian systems      58 ff. 95 121 135
Periodic solutions, of semilinear wave equation      61 ff. 116 135
Periodic solutions, with prescribed minimal period      96 f.
Perron's method      16
Plateau problem      19 ff. 191
Plateau problem, boundary condition      19
Pohozaev identity      140 156
Poincare inequality      214 f.
Pseudo gradient flow      76 see
Pseudo gradient vector field      73 78
Pseudo gradient vector field, for non-differentiable functionals      138
Pseudo gradient vector field, on convex sets      149
Pseudo — Laplace operator (p-Laplacian)      5
Regular point (value)      1 148
Regularity theory      16 32 54 216
Regularity theory, for minimal surfaces      24
Regularity theory, for the constant mean curvature equation      183
Regularity theory, in elasticity      30
Regularity theory, partial regularity for evolution of harmonic maps      197 ff. 210
Rellich — Kondrakov Theorem      213
Schauder estimates      216
Schwarz-symmetrization      40
Separation of spheres      154 197
Sobolev embedding (inequality)      40 ff. 155 201 211
Sub-additive      87
Sub-differential      55
Sub-solution      16
Super-solution      16
Supervariant      87
Support, support function      55
Support, support hyperplane      55
Symmetry      34 154
Symmetry group      see “Group action”
Symplectic structure      57
Technique, Fatou-lemma technique      32
Technique, hole-filling technique      53
Vanishing (of a sequence of measures)      37
Variational inequality      13 151
Volume      180 183
Wave equation      61 ff. 116 135
Yamabe problem      18 178
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