Page 241 - INTRODUCTION TO THE CALCULUS OF VARIATIONS

228 INDEX

Indicator function, 41 Poincaré-Wirtinger inequality, 54, 58,
Invariant Hilbert integral, 77 74, 75, 87, 96, 154, 155
Isoperimetric inequality, 6, 10, 153— Poisson equation, 148
155, 157—160, 163, 164 Polyconvex function, 100, 129
Isothermal coordinates, 129, 136, 137, Principal curvature, 132
140
Rellich theorem, 35
Riemann theorem, 143
Jacobi condition, 9, 47, 76
Riemann-Lebesgue Theorem, 19, 20
Jenkins-Serrin theorem, 147
Riesz Theorem, 17, 30
Jensen inequality, 40, 43, 50, 109
Schauder estimates, 148
Korn-Müntz theorem, 148
Scherk surface, 133
Kronecker symbol, 125
Second variation, 57
Sobolev imbedding theorem, 32, 34,
Lagrange multiplier, 57, 160
93, 97
Lagrangian, 5, 46, 68, 72
Stationary point, 9, 45, 48, 50, 62,
Laplace equation, 2, 5, 9, 81, 95,
69, 72
117, 118
Support function, 41
Legendre condition, 9, 47
Surface
Legendre transform, 40, 42, 46, 62
minimal, 5, 9, 28, 80, 85, 96,
Lipschitz continuous functions, 15
127, 129, 133—137, 145, 146,
Lower semicontinuity, 8, 20
160
minimal of revolution, 4, 5, 56,
Mean curvature, 6, 128, 129, 132,
133, 134
137, 147, 160, 168
nonparametric, 2, 5, 6, 10, 127—
Mean Value formula, 123
133, 135, 137, 145—147
Minimal surface equation, 6, 96, 128,
of the type of the disk, 131
146, 147, 151
parametric, 6, 127—130, 139
Minkowski inequality, 17, 23
regular, 131, 133, 134, 137, 140,
Minkowski-Steiner formula, 162, 164
145, 147
Mollifiers, 24
Variations of independent variables,
Newton problem, 4 60, 141
Null Lagrangian, 74
Weak form of Euler-Lagrange equa-
p-Laplace equation, 95 tion, 48
Parseval formula, 156 Weierstrass condition, 9, 47
Piecewise continuous functions, 14 Weierstrass E function, 76
Plateau problem, 5, 129, 130, 139— Weierstrass example, 52, 86
141, 144—146 Weierstrass-Erdmann condition, 9
Poincaré inequality, 37, 58, 80, 82, Weyl lemma, 118
89 Wirtinger inequality, 54, 153—155