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