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| Ladyzhenskaya O.A. — The Boundary Value Problems Of Mathematical Physics |
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| Предметный указатель |
Adjoint problem 54
Banach space 2
Boundary value problems of the first kind (Dirichlet) 50—58 71—77 261—266
Boundary value problems of the second kind (Neumann) and the third kind 61—65 266—270
Cauchy sequence 2
Characteristic surface 148
Closure of an inequality 24
Closure of an operator 10
Coercitivity 187
Compact set in the strong topology 3
Compact set in the weak topology 3
Completeness 2
Continuation by parameter 72—74
Convergence in the norm (strong convergence) 2
Convergence, weak 2
Dense set 2
Difference schemes 212—307
Difference schemes, alternating-direction 274—279
Difference schemes, approximate 302—305
Difference schemes, explicit 279
Difference schemes, implicit 251
Diffraction problems 196—201 301—302
Elliptic equation 44—102 241—247 261—270
Elliptic system 209
Embedding theorems 25—43
Embedding theorems for functions defined on grids 223—236
Finite difference method of Fourier 236—241
Fourier series in eigenfunctions of elliptic operators 58—61
Fourier’s method 128—132 174—181
Fredholm theorems 7 52—56 102
Functional method 83—84 170—174
Fundamental sequence 2
Galerkin’s method 77—83
Generalized derivative 10 12—18
Generalized solution of a boundary value problem 48 189—191
Generalized solution of an equation 47
Generalized solution of an initial-boundary value problem 109—113 122 160—174 322
Hilbert space 2
Hyperbolic equation 147—182 253—261 281—284
Inequalities for grid functions 223—236
Inequality, Cauchy — Schwarz 2 4—5
Inequality, energy 49 149—153
Inequality, first fundamental 49
Inequality, Garding’s 184
Inequality, Holder’s 5
| Inequality, multiplicative 34—43
Inequality, Poincare — Friedrich’s 23—24
Inequality, second fundamental 64—71 133—135
Inequality, triangle 4—5
Inequality, Young’s 4
Initial-boundary value problems of the first kind 104—121 149—161 271—294
Initial-boundary value problems of the second and third kinds 121—146
Integration by parts formula 32
Interpolations of grid functions 223—230
Laplace’s method 128—132 174—181
Least squares method 84—85
Norms for grid functions 223—235
Operator, adjoint 9
Operator, bounded 6
Operator, completely continuous 6
Operator, diffprence 219—223
Operator, self-adjoint 6
Operator, symmetric 9
Operator, unbounded 8—12
Parabolic equation 103—146 247—253 271—281
Precompact set in the strong topology 3
Precompact set in the weak topology 3
Rellich’s theorem 25
Riesz’s theorem 6
Ritz’s method 83—84
Rothe’s method 135—139
Schrodinger equation 194—196 300—301
Schrodinger operator 94
Separable space 2
Spaces (For definitions of spaces used) (see Basic Notation xxv-xxx)
Stokes 188
Stokes, strongly elliptic 183—191 296—297
Stokes, strongly hyperbolic 191 194
Stokes, strongly parabolic 191 194
Strong convergence 2
Summation by parts 221
Surface, characteristic 148
Surface, space-like 148
Surface, time-like 148
System, elasticity 297—299
System, Navier — Stokes 188 205
System, Oseen 188
Trace of a function on a surface 28—34
Velocity of propagation 149—155
Weak convergence 2
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