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Taylor M.E. — Partial Differential Equations. Nonlinear Equations (vol. 3)
Taylor M.E. — Partial Differential Equations. Nonlinear Equations (vol. 3)

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Название: Partial Differential Equations. Nonlinear Equations (vol. 3)

Автор: Taylor M.E.

Аннотация:

This is the third of three volumes on partial differential equations. It is devoted to nonlinear PDE. There are treatments of a number of equations of classical continuum mechanics, including relativistic versions. There are also treatments of various equations arising in differential geometry, such as in the study of minimal surfaces, isometric imbedding, conformal deformation, harmonic maps, and prescribed Gauss curvature. In addition, some nonlinear diffusion problems are studied. Analytical tools introduced in this volume include the theory of L^p Sobolev spaces, H lder spaces, Hardy spaces, and Morrey spaces, and also a development of Calderon-Zygmund theory and paradifferential operator calculus. The book is addressed to graduate students in mathematics and to professional mathematicians, with an interest in partial differential equations, mathematical physics, differential geometry, harmonic analysis and complex analysis.


Язык: en

Рубрика: Математика/Анализ/Дифференциальные уравнения/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1996

Количество страниц: 610

Добавлена в каталог: 23.04.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Absolute boundary condition      491
Area functional      130
Area functional, second variation      145
Arithmetic-geometric mean inequality      236 249
Ascoli’s Theorem      137
Bakelman’s estimate      223
Barrier      252
Barrier, lower      184
Barrier, upper      184
Belousov — Zhabotinski system      306
Bernoulli’s law      376 395 473 474
Bernstein’s Theorem      158
Besov space      53
Bianchi identity      533
Birkhoff’s theorem      541
Blow-up      365
Bochner Laplacian      493
Boltzmann equation      398
Boundary gradient estimate      181 204 248
Boundary problem, regular      165
Brusselator      303 307
Cacciopoli inequality      211
Calculus of variations      192
Calderon — Zygmund theorem      16
Catenoid      133
Cauchy — Kowalewsky theorem      387 457
Codazzi equation      144
Completely nonlinear      109 118 336 368 380
Concave      236
conformal      95 101
Conformal Laplacian      100
Conservation law      393 471
Conservation law, scalar      398
Conservation law, system      411 436 445
Constraint equations      589
Contraction mapping principle      100 272
Convex      92 193
Covering lemma, Calderon — Zygmund      17
Covering lemma, Vitali      207
Covering lemma, Wiener      77
Deformation tensor      485 493 589
DeGiorgi — Nash — Moser theory      169
Difference scheme      409
Dirichlet problem      91 110 168 180 288
div-curl lemma      27 73 83 447
Divergence form      122
Divergence theorem      529
Dust      526
Eddington — Finkelstein coordinates      542
Eikonal equation      442
Einstein tensor      525 538
Einstein’s equations      378 524 541
Einstein’s equations, initial-value problem      578
Elliptic      42 108
Elliptic boundary problem      159
Elliptic, strongly      198 236
Elliptic, underdetermined      113
Elliptic, uniformly      185
Elliptic, very strongly      198
Energy      282
Energy conservation      396
Enneper’s surface      134
Enstrophy      485
entropy      398 423
Entropy, condition      439
Entropy, inequality      401
Entropy, Kruzhkov’s condition      401
Entropy-flux pair      436 447
Equation of state      392 397 423
Euler characteristic      102
Euler equation      476 485
Euler equations      391
Euler’s equation      468 473
Exterior derivative      469
Finite propagation speed      369 383 403 587
Fisher equation      301
Fitzhugh — Nagumo equation      301
Fitzhugh — Nagumo equations      291 296 304 315
Fixed-point theorem, Brouwer      261
Fixed-point theorem, Leray — Schauder      98 254 262 594
Fixed-point theorem, Schauder      191 261
Fluid flow, compressible      371 383 390 412 420 423 440
Fluid flow, incompressible      467
Fluid flow, irrotational      395 474
Fluid flow, relativistic      533 563 585
Fluid flow, stationary      473
Fluid flow, steady      396
Fluid flow, viscous      493
Fourier transform      15
Friedrichs mollifier      3 328 360 476 490
Frobenius’s Theorem      474
Fuzzy function      66
Fuzzy function, sharply defined      67
Gagliardo — Nirenberg inequality      7 26
Galerkin method      367
Galerkin method, modified      328
Gauss curvature      95 101 146 158 244 249 254 381 538
Gauss map      159
Gauss — Bonnet formula      102 150 532 545
Gauss — Codazzi equations      587
Geometrical optics      441
Geometrical optics, nonlinear      444
Girding inequality      338 341
Glimm scheme      433 459
Gravitational collapse      572
Gravitational constant      571
Gronwall inequality      329 361 364 366 479
Gronwall’s inequality      311
Growth condition, controllable      199
Hamiltonian      554
Hardy space      77 221
Harmonic      132
Harmonic coordinates      124 213 579
Harmonic map      143 195 213 221 282
Harnack inequality      172 226 349
Hausdorff measure      204
Helicity      476
Helicoid      133
Helmholtz theorem      395 472
hessian      244
Hodge decomposition      84 468 474 486 491
Hodge laplacian      479 493
Hoelder continuity      173 232 236 350
Hoelder inequality, reverse      211
Hoelder space      37 115
Hoelder’s inequality      3
Holomorphic      133
Hopf theorem      498 511
Hyperbolic system      600
Hyperbolic system, genuinely nonlinear      414 456
Hyperbolic system, linearly degenerate      422
Hyperbolic system, second-order      376 579
Hyperbolic system, strictly      372 412 445 454
Hyperbolic system, symmetric      360 388 476
Hyperbolic system, symmetrizable      371
Implicit function theorem      103
Instability, diffusion-driven      302
Integral equation      272 316
Interpolation      5 22
Interpolation, Marcinkiewicz      16
Inverse function theorem      97
Isometric imbedding      113 125 131 195 282
Isothermal coordinates      96
Kelvin circulation theorem      394 471
Kepler problem      555
Kerr metric      553
Kerr — Newman metric      562
Killing field, conformal      589
Killing field, timelike      545
Kolmogorov — Petrovskii — Piskunov equation      301
Kruskal coordinates      543
Krylov — Safanov estimates      223
Laplace operator      95 131 201
Lapse function      597
Layer potential      516
Legendre — Hadamard condition      198
Leray projection      468
Lie derivative      392 469
Linearization      108
Liouville’s theorem      159
Liquid crystal      195
Littlewood — Paley theory      20 25 46
Local solvability      109
Longitudinal wave      419
Lorentz force law      527
Lorentz metric      525
Lower solution      101 244
Maximal function, grand      77
Maximal function, Hardy — Littlewood      77
Maximum principle      94 153 157 181 185 204 244 277 334
Maxwell — Einstein equations      560 583
Maxwell’s equations      526
Mean curvature      131 189
Mean curvature, prescribed      222
Mean curvature, vector      131
Membrane      186
Method of continuity      96 180 202 243
Minimal submanifold      130 288
Minimal surface      130 383
Minimal surface equation      152 168 184 203
Minimal surface, associated      133
Minimal surface, conjugate      133
Minimal surface, stable      150
Minimal surface, Weierstrass — Enneper representation      134
Minimization      192 202
Minimization, constrained      194
Monge — Ampere equation      109 243
Monge — Ampere equation, hyperbolic      381
Morrey space      174 257 258
Morrey’s lemma      182 209 259
Moser estimate      11 56 59 328 361 374 477
Moser estimates      293
Moser iteration      170 346
Murat’s lemma      447
Nash imbedding theorem      129
Nash — Moser estimates      336 344
Navier — Stokes equations      493 505
Neumann problem      290 487
No-slip boundary condition      505
Nonlinear Klein — Gordon equation      383
Oleinik condition (E)      405
Oppenheimer — Volkov equation      570
Orbit, heteroclinic      300 431
Orbit, homoclinic      300
Palatini identities      529
Parabolic      272 327 336
Parabolic, Petrowski      339
Paradifferential operator      55 60 119 337
Parametrix      32 115
Paraproduct      65
Partition of unity, Littlewood — Paley      20 37 47 54 259
Pattern formation      303
Plateau problem      135 222
Poincare disk      106
Poisson integral      137
Predator-prey equations      306
Pressure      392 469
Proper time      525
Pseudodifferential operator      15 46 372 479
Pseudodifferential operator, elliptic      517
Quasi-linear      108 117 180 327 338 344 360
Rankine — Hugoniot condition      404 415 431
Rarefaction wave      407 414
Reaction-diffusion equation      290
Reaction-diffusion equations      354
Regularity      115 159
Regularity, partial      204
Regularity, Schauder      117
Reissner — Nordstroem metric      562
Relativity      525
Rellich’s theorem      14 279
Ricci tensor      124 149 213 487 525
Riemann invariant      440 448 450
Riemann mapping theorem      135
Riemann problem      404 414
Riemann surface      106
Riemann tensor      487
Scalar curvature      525
Schwartz kernel      16
Schwarzschild metric      542 554 560
Second fundamental form      144 247 288 487
Sectional curvature      283
Semigroup, holomorphic      29
Semilinear      91 211 272 369
Shock interaction      434
Shock speed      415
Shock wave      406 418
Shock wave, spherically symmetric      436
Simple wave      436
Sine-Gordon equation      385
Sobolev imbedding theorem      4 23 33 39 276 285 329 361
Sobolev space      2
Soliton equations      444
Spacelike surface      378 579 580 588
Spacetime      524
Spacetime, spherically symmetric      534
Spacetime, static      541 549
Spacetime, stationary      545
Splitting method      308 315
Stefan Problem      315
Stirling’s formula      14
Stokes operator      506
Stream function      396
streamline      396 473
Stress tensor      493
Stress-energy tensor      525 533
Strong energy condition      532
Symbol      15 46
Symbol smoothing      51 58 60 337
Symmetrizer      371 444
Synge’s theorem      151
Theorema egregium      146
Timelike      525
Transport equation      442
traveling wave      298 433
Triebel space      53
Trotter product formula, nonlinear      297 308
Trudinger’s estimate      26
Trudinger’s inequality      13 104
Uniformization theorem      106 134
Upper solution      101 251
VACUUM      429
Vibrating membrane      459
Vibrating string      420 450 451 453
Viscosity method      398 432
Viscous profile      431
Vortex line      474
Vortex tube      394 472
Vortex tube, strength of      395
Vorticity      392 469 564
Vorticity equation      393 469 474 565
Vorticity equation, Lichnerowicz      566
Wave map      387
Weingarten formula      130 145
Weitzenbock formula      492 494 589
Yamabe problem      99
Young measure      67 446
Young’s inequality      48 53
Zygmund space      38 43 115 259 480
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