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Evans L.C. — Partial Differential Equations
Evans L.C. — Partial Differential Equations

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Название: Partial Differential Equations

Автор: Evans L.C.

Язык: en

Рубрика: Математика/Анализ/Дифференциальные уравнения/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1998

Количество страниц: 662

Добавлена в каталог: 29.10.2004

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
A priori estimates      504
Action functional      116
Adjoint      639
Adjoint of elliptic operator      302
Adjoint, bilinear form      302
Admissible states      589
Airy's equation      4 173
Almost everywhere      646
Almost separably valued function      650
Amplitude      207
Analyticity      226—233
Analyticity of harmonic functions      31
Analyticity of solutions to heat equation      62
Analyticity of solutions to PDE      229
Arzela — Ascoli compactness criterion      274 455 540 634
Asymptotics      157 199—221
Averages      616
Backwards uniqueness, heat equation      63
Banach space      241 249 635
Barenblatt's solution      182
Barrier      346
Basis of eigenfunctions      169 335 353 360 363 364 388 390 391 493
Basis, orthonormal      637
Beam equation      4
Bernoulli's law      196
Bessel potential      187
Biharmonic equation      345
Bilinear form      296
Bilinear form, estimates for      299—301
Bilinear form, time-dependent      351 378 403
Bistable equation      175
Blow-up, conservation law      597
Blow-up, nonlinear heat equation      513
Blow-up, porous medium equation      171
Bochner's theorem      650
Boundary      626
Boundary data, admissible      106
Boundary data, compatibility conditions on      104
Boundary data, noncharacteristic      104 106
Boundary, $C^k$      626
Boundary, analytic      626
Boundary, normal to      626
Boundary, straightening      103 224 228 320 325 627
Boundary-value problem, eigenvalue problem      334
Boundary-value problem, homogenization of      218
Boundary-value problem, Laplace's equation      41
Boundary-value problem, nonlinear boundary conditions      489
Boundary-value problem, nonlinear eigenvalue problem      464
Boundary-value problem, nonlinear Poisson equation      507 518
Boundary-value problem, Poisson's equation      27 42
Boundary-value problem, quasilinear elliptic equation      491 505
Boundary-value problem, second-order elliptic equation      293 296
Boundary-value problem, sernilinear elliptic equation      482 514
Browder — Minty method      497 540
Burgers' equation      5 140 141 143
Burgers' equation, vanishing viscosity      204
Burgers' equation, viscous      195
Calculus of variations      11 43 117 123 431—490
Cauchy data      222
Cauchy problem for boundary data      222
Cauchy problem for heat equation      47
Cauchy sequence      241 249 635
Cauchy — Kovalevskaya Theorem      10 228—233
Chain rule      291
Characteristic equation      398
Characteristics      10 19 97—115 152 200 217 399
Characteristics and boundary conditions      103—106
Characteristics and local solution to PDE      106—110
Characteristics, applications of      110—115
Characteristics, crossing      112
Characteristics, derivation      97
Characteristics, examples of      99—102
Characteristics, projected      98
Characteristics, summary of characteristic ODE      98
Clairaut's equation      93
Closed graph theorem      417 638
Coarea formula      396 628
Coercivity      443 453
Cofactor matrix      411 440
Compact embeddings      271
Compact linear operator      640
Compact mapping      503
Complete integral      92
Complete linear space      635
Condition E      612
Conservation law      5 8 10 136—162
Conservation law, characteristics for      112 143
Conservation law, decay in sup-norm      157
Conservation law, decay to N-wave      158
Conservation law, derivation      567
Conservation law, implicit solution      114
Conservation law, initial-value problem      136
Conservation law, integral solution      137 148
Conservation law, Lax — Oleinik formula      146
Conservation law, Rankine — Hugoniot condition      140
Conservation law, systems      6 12 567—606
Conservation law, viscous      234
Constitutive relation      569 578 595
Constraints, incompressibility      472
Constraints, integral      463
Constraints, one-sided      467
Constraints, pointwise      470
Contraction      499 501 529
Contraction, semigroup      414
Control theory      551
Controls, admissible      551
Controls, optimal      11 560
Converting nonlinear into linear equations      194—199
Convex function      523 621
Convex function, domain      523
Convex function, subdifferential of      163 523
Convex function, supporting hyperplane      621
Convexity      447
Convexity, uniform      131 143 144 621
Corrector problem for Green's function      34
Corrector problem for homogenization      221
Cost      552
Cost, running      552
Cost, terminal      552
Courant minimax principle      347
Crandall, M. — Lions, P.-L.      564
critical exponent      486 514
Critical point      118 432 476—481
Critical value      477
Curvature      201
Curvature, mean      435 489
Curvature, principal curvatures      216
Cutoff function      310
d' Alembert's formula      68 69 78 82 88
Deformation Theorem      477 481
DeGiorgi — Nash estimates      462
Degree      487
Derrick — Pohozaev identity      517
Difference quotients      277—279
Difference quotients and weak derivatives      277
Difference quotients, definition of      277
Differential equations in Banach spaces      413
Differential equations in Hilbert spaces      479 528
Diffusion      200
Diffusion and transport      199—204
Diffusion, equation      4 44
DiPerna, R.      165
Dirac measure      25 35 48 200 201
Dirichlet's boundary condition      294
Dirichlet's principle      42 434
Dirichlet's principle, generalized      434
dispersion      173
Dissipation      173
Divergence form PDE      294 350
Domain of dependence, generalized wave equation      395
Domain of dependence, wave equation      84
Dominated Convergence Theorem      134 154 211 412 452 510 606 648
Doubling variables      547 608
Doughs, A.      165
Dual space      638
Dual space of $H^{1}_{0}$      283
Duality of Hamiltonian and Lagrangian      122
Duhamel's principle      49 81
Dynamic programming      11 551 552
Egoroff's theorem      446 647
Eigenfunction      169 305
Eigenfunction, basis      335
Eigenvalue      11 169 305 334 574 575 638
Eigenvalue, nonsymmetric elliptic operator      340—344
Eigenvalue, principal      11 336—344 512 537
Eigenvalue, symmetric elliptic operator      334—340
Eigenvector      334 575 638
Eigenvector, left      574
Eigenvector, right      574
Eikonal equation      5 93 96 564
Eikonal equation, generalized      395
Elasticity, linear      6
Elasticity, nonlinear      457 475
Elliptic regularization      487
Ellipticity      294
Energy estimates, quasilinear elliptic equation      494
Energy estimates, second-order elliptic equation      299
Energy estimates, second-order hyperbolic equation      381
Energy estimates, second-order parabolic equation      354
Energy estimates, symmetric hyperbolic system      405
Energy methods, heat equation      62—65
Energy methods, Laplace's equation      41—43
Energy methods, wave equation      83—85
Entropy condition      12 143 149 589 599
Entropy condition, Lax's      589
Entropy condition, Liu's      602
Entropy solution, single conservation law      150
Entropy solution, system      604 607
Entropy/entropy-flux pair      604 607
Envelopes      94
Envelopes, construction of solutions using      94
Equipartition of energy      88
Essential supremum (ess sup)      648
Euler equations      569 578
Euler equations, barotropic      595 611
Euler equations, incompressible      6 196
Euler — Lagrange equation      434 450
Euler — Lagrange equation system      454
Euler — Lagrange equation systems      438
Euler — Lagrange equation, harmonic maps      470
Euler — Lagrange equation, one-dimensional      117
Euler — Poisson — Darboux equation      70 75
Euler's formula for Jacobians      476
Exponential solutions      172
Extensions      254—257
Factoring PDE      67 398
Fatou's lemma      532 648
Feedback control      553
First variation      433
First-order equation      9 91—165
First-order equation, complete integral      92
First-order equation, notation for      91
First-order hyperbolic system      11 400—412
Fixed point theorem, Banach's      498 500 502 537
Fixed point theorem, Brouwer's      441 493
Fixed point theorem, Schaefer's      342 503 507
Fixed point theorem, Schauder's      502
Fixed-point methods      11 498—507
Fokker — Planck equation      4
Fourier transform      10 182—190 282—283 292 408
Fourier transform and Sobolev spaces      282
Fourier transform, applications      186—190
Fourier transform, definition of      183 184
Fourier transform, properties      183 184
Fredholm alternative      220 641 643
Free boundary problem      470
Fully nonlinear PDE      2
Function spaces $C^2_1$      618
Function spaces $C^k$      618
Function spaces $C^{k, {\gamma}}$      241
Function spaces $H^k$      245
Function spaces $H^k_0$      246
Function spaces $H^s$      283
Function spaces $H^{-1}$      283
Function spaces $L^P$      618 636
Function spaces $W^{k,p}$      244
Function spaces $W^{k,p}_0$      245
Function spaces BMO      276
Function spaces, Banach space-valued      285—289
Fundamental solution, heat equation      46 180 188
Fundamental solution, Laplace's equation      22 25
Fundamental solution, Schroedinger's equation      188
Galerkin's method      169 353 380 493
Gauss — Bonnet theorem      488
Gauss — Green Theorem      20 627
General integral      96
Generator of semigroup      414—418
Genuine nonlinearity      581 588 594
Geometric notation      614—615
Geometric optics      207—217 395
Gidas, B. — Ni, W. — Nirenberg, L.      538
Gradient flow      529
Green's formulas      33 34 628
Green's function      33—41
Green's function for ball      40
Green's function for half-space      37
Green's function, derivation of      33—35
Green's function, symmetry of      35
Hadamard's example      234
Hamilton — Jacobi equation      5 10 11 94 96 115—136 171 395 539
Hamilton — Jacobi equation, characteristics for      114 116 123
Hamilton — Jacobi equation, Hopf — Lax formula      124
Hamilton — Jacobi equation, semiconcavity condition      130
Hamilton — Jacobi equation, solution a.e.      128
Hamilton — Jacobi equation, uniqueness      132
Hamilton — Jacobi equation, weak solution      132
Hamilton — Jacobi — Bellman equation      557
Hamilton — Jacobi — Bellman equation and optimal controls      560
Hamilton's differential equations      115 116 120
Hamiltonian      119 557
Hamiltonian duality with Lagrangian      122
Harmonic function      20
Harmonic mapping      470
Heat ball      52
Heat equation      4 9 44—65 172
Heat equation, backwards uniqueness      63
Heat equation, derivation      44
Heat equation, energy methods      62—65
Heat equation, fundamental solution      46
Heat equation, infinite propagation speed      49
Heat equation, initial-value problem      47
Heat equation, maximum principle      57
Heat equation, mean-value formula      52
Heat equation, nonhomogeneous problem      44 49
Heat equation, nonlinear      511
Heat equation, regularity      59 61
Heat equation, strong maximum principle      54
Heat equation, uniqueness      56 58
Helmholtz's equation      3 305
Hilbert space      636
Hille — Yosida theorem      418 421 423
Hodograph transform      197
Hoelder spaces      240—241
Homogeneous PDE      2
Homogenization      218—221 235
Hopf — Cole transformation      195
Hopf — Lax formula      10 121—136 539 560—563
Hopf's Lemma      330 333 341 343 344 519
Huygens' principle      80
Hyperbolic system, constant coefficients      408—412
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