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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: Рубрика: Математика /Анализ /Дифференциальные уравнения /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 1996Количество страниц: 610Добавлена в каталог: 23.04.2005Операции: Положить на полку |
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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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