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Egorov Y.V., Shubin M.A. — Partial Differential Equations I (Foundations of the Classical)
Egorov Y.V., Shubin M.A. — Partial Differential  Equations I  (Foundations of the Classical)



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Название: Partial Differential Equations I (Foundations of the Classical)

Авторы: Egorov Y.V., Shubin M.A.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1991

Количество страниц: 259

Добавлена в каталог: 10.09.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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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 Schrodinger      17
Operator Schrodinger 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 strictly hyperbolic 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 operator2      6 42
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 of limiting absorption      189
Principle maximum of limiting amplitude      189
Principle maximum strong      165
Problem $\overline{\partial}$      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
Schrodinger, 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 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 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 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) $\mathcal{D} (\Omega)$      48
Space(s) $\mathcal{D}' (\Omega)$      50
Space(s) $\mathcal{E} (\Omega)$      48
Space(s) $\mathcal{E}' (\Omega)$      49
Space(s) $\mathcal{S} (\Omega)$      48
Space(s) $\mathcal{S}' (\Omega)$      49
Space(s) dual      49
Space(s) Frechet      23
Space(s) Hoelder      99
Space(s) of test functions      48
Space(s) Schwartz      48
Space(s) Sobolev      113
Space(s) Sobolev $H^{S_{comp} (X)}$      116
Space(s) Sobolev $H^{S_{loc} (X)}$      115
Space(s) Sobolev $H^{S} (\Omega)$      113
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 analytic singular      63
Support of a distribution      53
Support of a function      48
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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