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| Egorov Y.U. (Ed), Gamkrelidze R.V. (Ed) — Partial Differential Equations I: Foundations of the Classical Theory |
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Название: Partial Differential Equations I: Foundations of the Classical Theory
Авторы: Egorov Y.U. (Ed), Gamkrelidze R.V. (Ed)
Язык: 
Рубрика: Математика/
Статус предметного указателя: Готов указатель с номерами страниц
ed2k:
Год издания: 1991
Количество страниц: 259
Добавлена в каталог: 13.09.2008
Операции: Положить на полку |
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| Предметный указатель |
Operator, elliptic, in a region 42
Operator, elliptic, Petrovskij 42
Operator, essentially self-adjoint 211
Operator, Fredholm 108
Operator, Hill 218
Operator, hyperbolic 26 27 137
Operator, hyperbolic, at a point 43 136
Operator, hyperbolic, in a region 43 136
Operator, hyperbolic, in the direction of a vector 43
Operator, hyperbolic, symmetric 157
Operator, hypoelliptic 78
Operator, infinitesimal generator 180
Operator, Laplace — Beltrami 15
Operator, Laplacian 10
Operator, linear differential 7
Operator, local 69
Operator, maximal 212
Operator, minimal 212
Operator, monodromy 218
Operator, nonstrictly hyperbolic 26
Operator, ordinary differential, fundamental solution for 70
Operator, properly elliptic 106
Operator, scattering 195
Operator, Schroedinger 17
Operator, Schroedinger, one-dimensional 202
Operator, spectrum, discrete 17
Operator, strictly hyperbolic 27
Operator, strictly hyperbolic, at a point 136
Operator, strictly hyperbolic, in a region 137
Operator, strictly hyperbolic, in the direction of a vector 43
Operator, Sturm — Liouville 201
Operator, transposed 58
Operator, wave 18 196
Order of an equation 7
Order of an operator 7
Outer capacity 101
Overdetermined system 42
Overdetermined system, elliptic 42
Ovsyannikov's theorem 34
Ovsyannikov, L.V. 33 34
Palais, R.S. 113 242 246
Palamodov, V.P. 243 246
Paley — Wiener — Schwartz theorem 66
Paley, R.E.A.C. 24 66
Parabolic cylinder functions 240
Parabolic equation 38
Parabolic equation at a point 38
Parabolic equation in a region 38
Parabolic equation, Petrovskij 2b 44 163
Parabolic equation, Shilov 163
Parabolic system, Shilov 172
Parabolicity, index of 172
Partial differential equation, linear 7
Pauli, W. 19
Peetre, J. 246
Periodic condition 206
Periodic Problem 206
Permitted zone 218
Petrovskij 2b-parabolic equation 44 163
Petrovskij ellipticity at a point 42
Petrovskij ellipticity in a region 42 82
Petrovskij, I.G. 27 29 35 42 82 83 85—87 94 97 144 145 150 163 172 177—179 242 246
Phillips, R. 140 184 199 244 245
Pitaevskij, L.P. 207 218
Planck, M. 17 187
Plane wave method 145
Plane wave scattering 192
Plane, noncharacteristic 26
Poincare, H. 18
Point, regular boundary 103
Point, Weyl limit 214
Poisson's equation 14 83
Poisson's formula 25 91 142 146 169
Poisson, S.D. 14 25 72 88 91 99 142 169
Polynomial(s), Chebyshev 238
Polynomial(s), Chebyshev, of first kind 238
Polynomial(s), Chebyshev, of second kind 238
Polynomial(s), Hermite 239
Polynomial(s), hyperbolic 26
Polynomial(s), Laguerre 239
Polynomial(s), Legendre 144
Polynomial(s), nonstrictly hyperbolic 26
Potential double-layer 64 95
Potential heat 76
Potential Newtonian 63 94
Potential retarded 76
Potential single-layer 64 95
Potential volume 63 94
Principal symbol of a differential operator 26 42
Principle of limiting absorption 189
Principle of limiting amplitude 189
Principle, Duhamel's 76 144
Principle, Huyghens' 145
Principle, maximum 24
Principle, maximum, for a general elliptic equation 104
Principle, maximum, for a parabolic equation 164
Principle, maximum, for harmonic functions 87
Principle, maximum, strong 165
Problem,  20
Problem, antiperiodic 206
Problem, boundary-value 11
Problem, boundary-value, regularly elliptic 131
Problem, boundary-value, self-adjoint 131
Problem, Cauchy 22 24—27
Problem, Cauchy, for an equation with constant coefficients 25
Problem, Cauchy, for the heat equation 24 25
Problem, Cauchy, for the one-dimensional wave equation 22
Problem, Cauchy, uniformly well-posed 177
Problem, Dirichlet 104
Problem, Dirichlet, exterior 93
Problem, Dirichlet, for Laplace's equation 24
Problem, Dirichlet, generalized statement 123
Problem, Dirichlet, interior 87
Problem, eigenvalue 126
Problem, mixed parabolic 132
Problem, Neumann 87
Problem, Neumann, exterior 93
Problem, Neumann, generalized statement 123
Problem, oblique derivative 109
Problem, periodic 206
Problem, regularly elliptic 131
Problem, scattering 192
Problem, self-adjoint 201
Problem, self-adjoint, regular 201
Problem, Sturm — Liouville 202
Problem, well-posed 24
Product, direct, of distributions 61
Product, direct, of functions 61
Product, tensor, of distributions 61
Product, tensor, of functions 61
Properly elliptic operator 106
Quasimomentum 219
Radiation condition, Sommerfeld 185
Radon measure 54
Radon transform 146
Radon, J. 54 146
Ray, geometric-optical 191
Rayleigh, J.W. 135
Reed, M. 199 204 211 242 246
Reflection, coefficient of 218
Refraction, conical 157
Regular boundary point 103
Regularization of a generalized function 52 60
Relations, completeness 211
Relations, orthogonality 210
Removable singularities theorem 81—82 92
Rempel, S. 110 111 242 246
Retarded potential 76
Riemann, G.F.B. 15 41 70 241
Riesz, F. 54 125
| Rodrigues' formula 225
Rodrigues, V.O. 225
Rolle, M. 225
Rudin, W. 23 47 51 53 65 242 246
Sakamoto, R. 246
Samarskij, A.A. 8 9 13 88 89 189 225 226 234 235 243 246
Sargsyan, I.S. 206 214 217 220 243 245
Scattering amplitude 193
Scattering matrix 198
Scattering of a plane wave 192
Scattering operator 195
Scattering problem 192
Schauder estimates 100
Schauder, J.P. 99 100
Schechter, M. 35 113 122 132 134 177 242 243
Schmidt, E. 204
Schrddinger, E. 16 17 19 150 182 186 196 202 210
Schroedinger equation 16 186
Schroedinger equation, steady-state 17
Schroedinger operator 17
Schroedinger operator, one-dimensional 202
Schulze, B.-W. 110 111 242 246
Schwartz kernel theorem 68
Schwartz space 48
Schwartz, J.T. 202 243 244
Schwartz, L. 24 47 51 53 55 57 65 66 68 242 246
Sears' theorem 213
Sears, D.B. 213
Seidenberg, A. 79
Self-adjoint problem 131
Semigroup, infinitesimal generator of 180
Separation of variables 135 163
Sequence, delta-shaped 51
Sequential completeness 51
Series, hypergeometric (Gauss') 241
Shapiro — Lopatinskij condition 107
Shapiro, Z.Ya. 105
Sheaf 53
Shilov, G.E. 47 51 53 55 57—59 62 65 69 71 73 78 83 132 163 164 172 242 244 246
Shilov-parabolic equation 163
Shubin, M.A. 195 211 213 216 242 243 246
Simon, B. 199 204 211 242 246
Single-layer potential 53
Singular integral 65
Singularity, weak 98
Smirnov, V.I. 88 90 94 97 242 243 246
Sobolev spaces 113
Sobolev spaces, anisotropic 132
Sobolev spaces, local 115
Sobolev, S.L. 24 113 117 119 131 243 246 247
Sokhotskij's formulas 52
Sokhotskij, Yu. B. 52
Solomyak, M.Z. 113 211 243
Solonnikov, V.A. 113 132 175 242 247
Solution of a hyperbolic equation, discontinuous 153—157
Solution of the Cauchy problem 71 171
Solution of the Cauchy problem, asymptotic 153
Solution of the Cauchy problem, for second-order equation with variable coefficients 171
Solution of the classical Dirichlet problem 87
Solution of the Neumann problem 87
Solution, fundamental 69
Solution, fundamental, for an operator 69
Solution, fundamental, for an ordinary differential operator 70
Solution, fundamental, for the Cauchy — Riemann operator 70
Solution, fundamental, for the D'Alembertian 72
Solution, fundamental, for the heat conduction operator 72
Solution, fundamental, for the Laplacian 70 83
Solution, generalized (weak) 123
Solution, generalized (weak), of a mixed boundary-value problem 161
Solution, weak (generalized) 123
Sommerfeld radiation condition 185
Sommerfeld's formula 235
Sommerfeld, A. 185 235
Source function for a Sturm — Liouville problem 202
Source function for the Dirichlet problem 88
Space(s) of test functions 48
Space(s),  50
Space(s),  48
Space(s),  49
Space(s),  48
Space(s),  49
Space(s),  48
Space(s), dual 49
Space(s), Frechet 23
Space(s), Hoelder 99
Space(s), Schwartz 48
Space(s), Sobolev 113
Space(s), Sobolev,  113
Space(s), Sobolev,  116
Space(s), Sobolev,  115
Space(s), Sobolev, anisotropic 132
Space(s), Sobolev, local 115
Space-like 159
Special functions 220—241
Spectrum of an operator, discrete 17
Spherical harmonics 220
Stegun, I.A. 243
Stein, E.M. 243 247
Steinhaus, H.D. 51
Steklov's theorem 204—205
Steklov, V.A. 205
Stieltjes, T.J. 54
Stokes G.G. 68 84 128
Stone's theorem 182
Stone, A. 182
Strang, G. 138 244
Strictly hyperbolic operator, in the direction of a vector 43
Strictly hyperbolic system, in the direction of a vector 43
Strong discontinuity 155
Sturm — Liouville operator 201
Sturm — Liouville problem 202
Sturm's theorem 206
Sturm, J.C.F. 201 202 205 206
Subsets, arithmetic sum of 63
Subspace, defect 212
Sum of subsets, arithmetic 63
Support of a distribution 53
Support of a function 48
Support, analytic singular 63
Surface, characteristic 33
Surface, space-like 159
Symbol, principal, of a differential operator 26 42
System, Cauchy — Riemann 20
System, complete linearly independent 200
System, Douglis — Nirenberg elliptic 43
System, Douglis — Nirenberg elliptic, at a point 42
System, Douglis — Nirenberg elliptic, in a region 42
System, Douglis — Nirenberg elliptic, Petrovskij 42
System, Hamiltonian 191
System, of electrostatic equations 43
System, overdetermined 42
System, overdetermined, elliptic 42
System, Shilov-parabolic 172
System, strictly hyperbolic 43
System, strictly hyperbolic, in the direction of a vector 43
System, symmetric hyperbolic 44
Tarski, A. 79
Taylor, B. 29
Taylor, J.R. 132 199 243 247
Telegraph equations 16
Tempered distribution 49
Tensor product of distributions 61
Tensor product of functions 61
Test functions 48
Theorem, Cauchy — Kovalevskaya 28—36
Theorem, Flaschka — Strang 138
Theorem, Fredholm property, regularity of solutions, and an a priori estimate for elliptic problems 109
Theorem, Garding's 137
Theorem, Hadamard's 178
Theorem, Harnack's 88
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