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| Evans L.C. — Partial Differential Equations |
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| Предметный указатель |
Hyperbolic system, nonlinear 573
Hyperbolic system, symmetric 402—408
Hyperbolicity 398 401
Hyperbolicity for symmetric system 401
Hyperbolicity, strict 401 573 578 595
Hyperbolicity, uniform 403
Hyperelastic materials 457
Implicit function theorem 105 212 217 465 518 576 577 585 633
Incompressibility 472—476
Inequality with  622
Inequality, Cauchy — Schwarz 624 636
Inequality, Cauchy's 622
Inequality, Gagliardo — Nirenberg — Sobolev 10 262—266
Inequality, general Sobolev-type 269
Inequality, Gronwall's, differential form 624
Inequality, Gronwall's, integral form 625
Inequality, Harnack's 32 86 333 370
Inequality, Hoelder's 622
Inequality, interpolation 290
Inequality, Jensen's 621
Inequality, Minkowski's 249 623
Inequality, Morrey's 10 266—269
Inequality, Poincare's 265 275—276 448
Inequality, Young's 622
Inequality, Young's, with 622
Initial-value problem, Burgers' equation 140
Initial-value problem, conservation law 136 144 150 568 604 606
Initial-value problem, Hamilton — Jacobi equation 115 124 129 135 539 542 546 550 560
Initial-value problem, heat equation 47 188 191
Initial-value problem, quasilinear parabolic equation 194 540
Initial-value problem, Schroedinger's equation 188
Initial-value problem, telegraph equation 190
Initial-value problem, transport equation 18 85
Initial-value problem, viscous Burgers' equation 195
Initial-value problem, wave equation 67 189 192 208
Initial/boundary-value problem, beam equation 427
Initial/boundary-value problem, heat equation 57 88 168
Initial/boundary-value problem, parabolic equation 511
Initial/boundary-value problem, quasilinear parabolic equation 535
Initial/boundary-value problem, reaction-diffusion system 499
Initial/boundary-value problem, second-order hyperbolic equation 378
Initial/boundary-value problem, second-order parabolic equation 350
Initial/boundary-value problem, wave equation 69 83
Inner product 636
Integral solution 137 148 570 607
Integration by parts formula 627
Interior ball condition 330 519
Inverse function theorem 106 197 198 591 592 632
Inversion through sphere 39
Irreversibility 189 538
Irrotational fluid equations 197
k-contact discontinuity 588
k-rarefaction wave 582
k-shock wave 589
k-simple wave 580
Kirchhoff's formula 73
Kolmogorov's equation 4
Korteweg — deVries (KdV) equation 5 174
Kovalevskaya's example 235
Kruzkov, S. 612
Lagrange multiplier as eigenvalue 464
Lagrange multiplier as function 471
Lagrange multiplier, integral constraints 464
Lagrange multiplier, pressure as 472
Lagrangian 116 432 437
Lagrangian duality with Hamiltonian 122
Lagrangian null 439 441 487 488
Laplace transform 191—194 417
Laplace transform, applications 191—194
Laplace transform, definition of 191
Laplace's equation 3 9 20—43 295
Laplace's equation, analyticity 31
Laplace's equation, derivation 20
Laplace's equation, Green's function 33—41
Laplace's equation, Harnack's inequality 32
Laplace's equation, Liouville's Theorem 30
Laplace's equation, mean-value formulas 25
Laplace's equation, regularity 28 29
Laplace's method 204
Lax — Milgram Theorem 297 299 301 345 483 644
Lax —Oleinik formula 10 144—162 206
Lebesgue measure 645
Lebesgue point 186 649
Lebesgue's Differentiation Theorem 281 630 648
Legendre transform 121 122 561
Legendre transform, classical 198
Leibniz' formula 12 247
Linear degeneracy 581 587
Linear operator 637
Linear operator, bounded 637
Linear operator, closed 638
Linear operator, symmetric 335 639
Linear PDE 2
Liouville's equation 3
Liouville's theorem 30
Lipschitz continuity 616
Lipschitz continuity and differentiability a.e. 279
Lipschitz continuity and weak partial derivatives 279
Lower semicontinuity 523
Lower semicontinuity, weak 445 525
Majorants 227 231
Maximum principle 10
Maximum principle, Cauchy problem for heat equation 57
Maximum principle, strong 339 341
Maximum principle, strong heat equation 54
Maximum principle, strong Laplace's equation 27
Maximum principle, strong second-order elliptic equation 330—333
Maximum principle, strong second-order parabolic equation 375—377
Maximum principle, weak second-order elliptic equation 327—329
Maximum principle, weak second-order parabolic equation 368—370
Maximum principle, weak, Laplace's equation 25 26
Maxwell's equations 6 88
Mazur's theorem 449 525 639
Mean-value formulas, heat equation 52
Measurable function 647
Method of descent 74 79
Minimal surface equation 5 198 435
Minimax methods 347 480
Minimizer 433 438 443
Mollifier 250 629
Momentum, generalized 119
Monge — Ampere equation 5
Monotone Convergence Theorem 447 648
Monotone vector field 492
Monotonicity 11 524
Monotonicity, strict 497
Morse lemma 212
Mountain Pass Theorem 480 485
Moving plane method 521—522
Multiindices 12 617
Multinomial theorem 12 227
N-wave 159
Navier — Stokes equations 6
Neumann boundary conditions 345 425
Newton's law 66 119 569
Noncharacteristic boundary data 104 106
Noncharacteristic surface 223 224 226
Nondiverggnce form PDE 294 350
Nonexistence of solutions 511—517
Nonhomogeneous problem, heat equation 49 51
Nonhomogeneous problem, transport equation 19
Nonhomogeneous problem, wave equation 81
Nonlinear eigenvalue problem 464
Norm 241 635 636
Normal derivative 627
Normal to surface 626
Notation for estimates 619
Notation for functions 615—619
Notation for matrices 613—614
Null Lagrangian 439 441 487 488
| O, o notation 619
Obstacle problem 467
Oleinik, O. 165
Optimality conditions 553
Orthogonal elements 637
p-Laplacian 5
p-system 568 606
p-system, traveling waves for 602
Palais — Smale condition 477 478 480 484
Parabolic approximation 204
Parabolic boundary 52
Parabolic cylinder 51
Parabolicity 350
Partial differential equation, definition of 1
Partition of unity 251 253 256 260 290
Penalty method 537
Perron — Probenius Theorem 334
Phase 207
Phase plane 176
Plancherel's Theorem 183
Plane wave 172 401
Poisson's equation 20 23 295
Poisson's equation, nonlinear 5 435
Poisson's formula, ball 41 86
Poisson's formula, half-space 37 87
Poisson's formula, wave equation 74 80
Poisson's kernel, ball 41
Polar coordinates 628
Polyconvexity 456
Porous medium equation 5 170 180
Porous medium equation, Barenblatt's solution of 182
Potentials 196 198
Projected characteristics 98
Propagation speed 182
Propagation speed, finite 78 84 163 394—397
Propagation speed, infinite 49 375
Proper function 523
Quasilinear PDE 2
Rademacher's Theorem 128 281
Radial solution 22
Rankirie — Hugoniot condition 140 141 144 572
Rarefaction curve 580
Rarefaction wave 141 582
Rayleigh's formula 336
Reaction-diffusion equation 511
Reaction-diffusion equation, bistable 175
Reaction-diffusion equation, scalar 5
Reaction-diffusion equation, system 6 499
Reflection 69 255 521
Reflexive space 638
Regularity 8
Regularity, heat equation 59 61
Regularity, Laplace's equation 28 29
Regularity, minimizers 458—462
Regularity, second-order elliptic equation 308—326
Regularity, second-order hyperbolic equation 387—393
Regularity, second-order parabolic equation 358—367
Rellich — Kondrachov Compactness Theorem 272
Resolvent 191
Resolvent set 417 638
Resolvent, identity 417
Resolvent, nonlinear 526
Response of system to controls 551
Retarded potential 82
Riemann invariants 593—599
Riemann invariants, blow-up 597
Riemann's problem 12 154—157 579—592
Riemann's problem, local solution of 590
Riesz representation theorem 284 298 299
Scalar conservation law 570
Schauder estimates 462
Schroedinger's equation 4 173 234
Second variation 436 488
Second-order elliptic equation 10 293—347
Second-order elliptic equation, bilinear form for 296
Second-order elliptic equation, boundedness of inverse 306
Second-order elliptic equation, eigenvalues and eigenfunctions 334—344
Second-order elliptic equation, existence theorems 301—306
Second-order elliptic equation, Harnack's inequality 333
Second-order elliptic equation, maximum principles 326—333
Second-order elliptic equation, regularity 308—326
Second-order elliptic equation, regularity, boundary 316—326
Second-order elliptic equation, regularity, interior 309—316
Second-order hyperbolic equation 11 377—400 402
Second-order hyperbolic equation as semigroup 423
Second-order hyperbolic equation in two variables 397—400
Second-order hyperbolic equation in two variables, canonical forms 399
Second-order hyperbolic equation, finite propagation speed 394—397
Second-order hyperbolic equation, regularity 387—393
Second-order hyperbolic equation, weak solution of 380—387
Second-order parabolic equation 11 349—377
Second-order parabolic equation as semigroup 421
Second-order parabolic equation, Harnack's inequality 370—374
Second-order parabolic equation, maximum principles 367—377
Second-order parabolic equation, regularity 358—367
Second-order parabolic equation, weak solution of 351—358
Semiconcavity 130 131
Semigroup 191
Semigroup, linear 11 412—424
Semigroup, nonlinear 11 523 528—536
Semilinear PDE 2
Separable space 636
Separation of variables 167—171
Shallow water equations 570 611
Shock set 583
Shock wave 8 140 143 573 583 589 599 600 604
Shock wave, nonphysical 141 589
Signature of matrix 210
Similarity solutions 45 172—182
Simple function 649
Simple waves 579
Singular integral 95
Singular perturbation 199
Sobolev inequalities 261—271
Sobolev space 10 241—292
Sobolev space, approximation by smooth functions 250—254
Sobolev space, compactness 271—274
Sobolev space, completeness of 249
Sobolev space, convergence in 245
Sobolev space, definition of 244
Sobolev space, differentiability a.e. 280
Sobolev space, extensions 254—257
Sobolev space, fractional 283
Sobolev space, norm 245
Sobolev space, traces 257—261
Soliton 175
Solution, classical 7
Solution, weak 8 508 542
Sound speed 579 595
Spectrum 305 638
Spectrum, compact operator 643
Spectrum, compact, symmetric operator 644
Spectrum, complex 340
Spectrum, point 638
Spherical means 67 70
Star-shaped level sets 517
Star-shaped set 514 515
State of system 551
State space 568
Stationary phase 208—217
Stokes' problem 472
Strain, stress 578
Strict hyperbolicity 573
Strongly measurable function 649
Subdifferential 523
Subscripts, superscripts 438 619
Subsolution 88 327 346 508 537
Summable function 647
Supersolution 327 508 537
System of partial differential equations 2
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