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| Bergman S., Schiffer M. — Kernel Functions and Elliptic Differential Equations in Mathematical Physics |
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| Предметный указатель |
 -metric 273 344
 -kernel 313
 transformation 337
transformation, scalar product 339
 transformation 316
transformation, complete continuity 324
transformation, properties 338—41
 transformations 341
transformations, eigenfunctions 346
transformations, involutory character 342
transformations, saltus condition 343
 -kernel 109 369
 -transform 345—346
 linear space 260
-monogenic functions 134
Adiabatic equation of state 135
Adiabatic gas, theory of 139
Airy stress function 247
Almansi, E. 232
Ampere's law 165—166
Analytic functions 72
Analytic functions, generalized 134
Associated partial differential equations 125—128
Axially symmetric flow 119
Bateman, H. 3
Bending of thin plates 232
Bergman, S. 116 119 132 141 147 206 229 236 246 297 355 402
Bergman, S., and Schiffer, M. 246 275 280 309 315 346 351 371 384 388
Bernoulli's equation 29 30 72 128
Bers, L., and Gelbart, A. 133 134 141
Betti's formulas 219 222
Bieberbach, L. 93 105 283
Biharmonic equation 229 232 234 235 247
Biharmonic equation, boundary value problems 236—237 242
Biharmonic equation, complex kernel 243
Biharmonic equation, complex solutions 243
Biharmonic equation, fundamental singularity 237
Biharmonic equation, fundamental solutions 238
Biharmonic equation, Green's function 238—239 244
Biharmonic functions 229
Biharmonic functions, representation of 229 238—240 241 243
Blasius formula, compressible flows 153—154
Blasius formula, force 88
Blasius formula, moment 90
Bochner, S. 119
Bolza, O. 105 108
Boundary value problems, elasticity 218 223—224
Boundary value problems, elasticity, plane strain 249 254
Boundary value problems, elasticity, thin plates 236
Boundary value problems, fluid flow, axially symmetric 122—123
Boundary value problems, fluid flow, compressible 141—145
Boundary value problems, fluid flow, incompressible 30 37
Boundary value problems, fluid flow, plane flows 77 82
Boundary value problems, heat conduction 4—7 12—16 22
Boundary value problems, Laplace's equation 9 19 30 31 77 79 82 110 168 199
Boundary value problems, of the first kind 50 77
Boundary value problems, of the second kind 57 77
Boundary value problems, of the third kind 267
Boundary value problems, statements and solutions for,  263—238 271—272
Boundary value problems, statements and solutions for,  263—238
Boundary value problems, statements and solutions for, associated partial differential equations 125
Boundary value problems, statements and solutions for, biharmonic equation 236—237 242—243
Boundary value problems, where the domain is, a circle 82
Boundary value problems, where the domain is, infinite 38
Boundary value problems, where the domain is, non-schlicht 149
Boussinesq, J. 232
Branch points 76 136
Built-in edge 236
Capacity see Electrostatic capacity
Caratheodory, C. 108
Cauchy — Riemann equations 72 73 77
Cauchy — Riemann equations, generalization 124
Chaplygin, S.A. 135 136
Charge coefficient 187
Charge density 155
Circulation 76
Circulation constant 89
Circulation constant, determination of 91
Cisotti, L 28 71
Coefficient of heat conductivity 1
Coefficient of heat conductivity, discontinuity 15
Coefficients, of mapping function, variational formulas 101—102
Complete continuity 323
Complete systems 116 202 226 241 243 249
Complete systems, construction of 282—5 286—297
Complete systems, for 280
Complete systems, of eigenfunctions 324 347—348 352
complex derivative 72
Complex differential operators 111
Complex kernel function 112—118 243—246
Complex potential 74
Compressible fluid flow 128—154
Compressible fluid flow, approximate solution 144
Compressible fluid flow, boundary value problems 141—145
Compressible fluid flow, Chaplygin's solutions 135
Compressible fluid flow, construction of solutions in hodograph plane 133—141
Compressible fluid flow, non-linear differential equation 129
Conducting surface, polarization 191
Conductor potential, of a surface, by itself 174
Conductor potential, of a surface, with respect to a domain 158 195
Conductor potential, relation to capacity 185
Conductor potential, relation to Green's function 185 187
Conductor system, forces and moments 197
Conformal mapping, Riemann's theorem 80 84
Conjugate functions 73
Conservation of energy 155 162
Conservation of mass 26 30 32 33
Conservative forces 28
Continuity equation 26 72 128
Continuous source distribution 9 33
Courant, R. 20 119 261 315 371;
Courant, R., and Hilbert, D. 7 20 71 178 260 261 265 269 273 292 311 326 331 332 385
D'Alembert's paradox 88
Davis, P. 355
Dead water regions 65 103
Dead water regions, existence proof 104
Deformation tensor 208
Diaz, J.B., and Weinstein, A. 56
Dielectric coefficient 155
Differential equations, elastic state 215
Differential equations, elastic state, plane strain 247
Differential equations, elastic state, thin plates 234
Differential equations, electrostatic field 155
Differential equations, fluid flow 25—28
Differential equations, fluid flow, axially symmetric 119—120 124
Differential equations, fluid flow, compressible 128—129 132
Differential equations, fluid flow, incompressible 30
Differential equations, fluid flow, irrotational 29 30
Differential equations, fluid flow, stationary 29 30
Differential equations, fluid flow, two-dimensional 72 73
Differential equations, heat transfer 2
Differential equations, heat transfer, endothermal reaction 21
Differential equations, heat transfer, homogeneous body 3 4
Differential equations, heat transfer, steady flow 3 4
Differential equations, magnetostatic field 166
Differential operators, complex 111
Diffusion 3
Dilatation, axes 208
Dilatation, principal 208
Dipole 8 33 75
Dipole flow, complex potential 85
Dipole, at infinity 35 41 75
Dipole, axially symmetric case 122
Dipole, two-dimensional complex 75
Dirichlet identities 46 297
Dirichlet product 47 259 297
Dirichlet's integral 17 20 21 23 31 47 161 216 259 273
Dirichlet's integral, definition 20
Dirichlet's integral, monotonic property 20
Dirichlet's principle 19 372
| Discontinuity surfaces 15 64 70
Displacement vector field 206
Dominants, method of 138 289
Doubly-orthogonal systems 352
Doubly-orthogonal systems, application of continuation problems 355
Doubly-orthogonal systems, completeness 354
E-metric 259
Eigenfunctions see Complete systems
Eigenvalues, estimates 391
Eigenvalues, stability 388
Elastic body, differential equation 215
Elastic potential 212
Electrostatic capacity 185
Electrostatic capacity, expressed by Green's function 186
Electrostatic capacity, lower bounds 188 204
Electrostatic capacity, relation to conductor potential 185 186 203
Electrostatic capacity, relation to harmonic kernel 203—204
Electrostatic field, energy 161
Electrostatic field, energy, general equations 155
Electrostatic field, energy, minimum principle 162
Electrostatic polarization 54 191
Electrostatic polarization potential 189
Electrostatic polarization tensor 53 191
Electrostatic polarization, inequalities for 54 193
Endothermal processes 21
Energy integral 258—259
Energy, elastic body 215
Energy, electrostatic field 161
Energy, fluid flow 31 44 86
Energy, plane strain 247—248
Energy, polarization 192
Energy, reaction field 190—192
Energy, thin plates 234—235
Equation of continuity 26 72 128
Equation of state 25 29
Equation of state, adiabatic 135
Equilibrium conditions, elastic bodies 210
Equilibrium conditions, thin plates 234
Error term, for kernel function 355—357
Existence proof, for boundary value problem 371—81
Extremal functions 19 23 31 32 58 147 162 188 277 301
Extremum problems, lift 98
Extremum problems, virtual mass 56 66—69
Farrell, O. 285 286
Flow patterns 33 35 74 76 136
Fluid dynamics, fundamental equations 25—28
Fluid flow, axially symmetric 119
Fluid flow, compressible two-dimensional 128
Fluid flow, incompressible 29 30 71
Fluid flow, irrotational 28 30 72
Fluid flow, stationary 28 30
Fluid flow, two-dimensional 71
Fluid flow, walled-in region 32
Fluids, non-viscous 25
Flux integral 262
Forces, mass 209
Forces, surface 209
Frank, P., and Mises, R. v. 3 7 28 71 157 178 236 246 273
Frechet, M. 261
Fredholm, J. 226 313 333 334
Free boundaries 66
Free boundaries, as extremal problem 66—70
Free boundaries, characterizations 65 67 68
Free boundaries, existence proofs 68
Free boundaries, plane flow 103
Free edge 236
Friedrichs, K. 246; see also Mises and Friedrichs
Functional 18
Functional derivative 18 147
Fundamental functions 272
Fundamental singularity, axially symmetric flow 121
Fundamental singularity, biharmonic equation 237
Fundamental singularity, complex formula 74
Fundamental singularity, construction 392
Fundamental singularity, definition 10 269
Fundamental singularity, Laplace's equation in three variables 9
Fundamental singularity, Laplace's equation in two variables 74
Fundamental singularity, pseudo-logarithmic plane 149
Fundamental singularity, used to construct a complete orthonormal system 282—285
Fundamental solutions 10 35 272
Fundamental solutions, biharmonic equation 238
Fundamental solutions, plane flows 76—81
Fundamental solutions, stability 384
Fundamental tensor fields 222
Fundamental tensor fields, construction 228—229
Galerkin, B.G. 232
Garabedian, P.R., and Schiffer, M. 108 119 381
Garabedian, P.R., and Spencer, D.C. 1U8
Garabedian, P.R., Lewy, H., and Schiffer, M. 108
Gelbart, A. 154; see also Bers and Gelbart
Geometric quantity 49 298
Goursat, E. 15 265 268 273 334
Green's formula, for functions of 270
Green's formula, three dimensions 2 11
Green's formula, two dimensions 260
Green's function, definition 12 78 263 270
Green's function, for  270
Green's function, for  12
Green's function, for biharmonic equation 238—239 244
Green's function, for Laplace's equation, in three dimensions 50 179
Green's function, for Laplace's equation, in two dimensions 78 263
Green's function, in the case of a circle 81 304
Green's function, in the case of infinite domains 50
Green's function, in the case of one argument at infinity 95 187
Green's function, inequalities for 22 52 179 360 366—368 383 386 393
Green's function, physical interpretation 12 179
Green's function, properties, conformal invariance 304
Green's function, properties, dependence on differential equation 386
Green's function, properties, dependence on domain 367
Green's function, properties, monotonicity 367 386
Green's function, properties, non-negativity 13 50 366
Green's function, properties, superadditivity 368
Green's function, properties, symmetry 50 78 263 271
Green's function, properties, unic multiplier 273
Green's function, relation to capacity 186
Green's function, relation to complex kernel function 112 245
Green's function, relation to conductor potential 185 187
Green's function, relation to mapping function 80
Green's function, series development 393
Green's function, used in deriving Poisson's formula 82
Green's function, used in solving boundary value problems 12 79 82 126 157 199 239 242 271
Green's function, variational and comparison formulas 95 194 364 366
Green's tensor field 222
Gunther, N.M. 15 261 268 273
Hadamard, J. 64 95 98 111 198 246 273 365 371
Hamel, G. 268
Harmonic functions, behavior at infinity 34—35
Harmonic functions, inequalities 40
Harmonic functions, representation by, -kernel 110
Harmonic functions, representation by, Green's function 79 199
Harmonic functions, representation by, Poisson's formula 82
Harmonic functions, singular points 33—35
Harmonic kernel function, three-dimensional case 198—206
Heat conduction 1
Heat equation 2
Heat equation, for a homogeneous body 3 4
Heat equation, for steady flow 3 4
Heat equation, modified 21
Hellinger, E., and Toeplitz, O. 268 326
Helmholtz, H. 64 65
Hilbert space 116 240 322
Hilbert space, fundamental theorem of linear transformations 324
Hilbert, D. 268 273 333 334 355 402;
Hodograph method 141
Hodograph plane 130
Hodograph plane, transition from 130—132 143—144
Hooke's law 213
Hopf, E. 262
Hurwitz, A., and Courant, R. 76
Hypergeometric series 140
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