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| Runst T. — Sobolev Spaces of Fractional Order, Nemytskij Operators, and Nonlinear Partial Differential Equations |
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| Предметный указатель |
Asymptote 432 439
atom 66
Bifurcation system 426 427
Boundary value problem, adjoint 131
Boundary value problem, regular elliptic 99
Boundary value problem, self-adjoint 132
Boundary value problem, semilinear elliptic 414
Codimension 127
Cokernel 129
Condition, Caratheodory 264
Condition, Landesman — Lazer 430 440
Condition, Michlin — Hoermander 23
Contraction 75
Core 450
de la Vallee Poussin mean 143
Degree, Brouwer 397
Degree, Leray — Schauder 399 409 513
Degree, Smale 508
Degree, topological 400 408
Derivative of composite functions 262 386
Diffeomorphism 18 73
Differential dimension 31
Distribution, Dirac 15 34 58 197 246
Distribution, ion-negative 137
Distribution, principal value 58
Distribution, real-valued 290
Distribution, regular 33
Distribution, singular 34
Distribution, tempered 6
Embedding, compact 14 82
Embedding, constant differential dimension 31
Embedding, constant smoothness 30
Embedding, continuous 14
Embedding, elementary 29
Embedding, set-theoretical 14
Fatou property 15
Fixed point isolated 409
Fourier multipliers 22
Fourier transform 6
Fredholm Alternative, nonlinear 428 431 436
Function space 1
Function, B-splines 48
Function, Caratheodory 264
Function, characteristic 49
Function, characteristic, cube 209
Function, characteristic, half-space 208
Function, characteristic, Sobolev mollification 55
Function, local singularity 43
Function, m-admissible 278
Half-space 72
Hausdorff measure 52
Hoermander classes 385
Homotopy 398
Homotopy, compact 400 409
Image 129
Index, fixed point 409 411 517
Index, Fredholm operator 129
Inequality, Gagliardo — Nirenberg 279
Inequality, Hardy 351
Inequality, Hoelder 239
Inequality, Moser 258
Inequality, Nikol'skij 32
Interpolation theory 85
Interpolation, complex method 86
Interpolation, couple 87
Interpolation, inequalities 87
Interpolation, nonlinear operators 87
Interpolation, property 86
Interpolation, real method 86 362
Interpolation, ±-method 87
K-functional 89
Kernel 129
Kernel, of type k 112
Lemma, alternative 425 426
Lemma, local representation 473
Lifting property 18
Localization property 69
Manifold,  472
Manifold, codimension 472
Map, proper 399 471 487
Map, suitable 424
Map, transversal 479
Maximal function 225
Maximal function, Hardy — Littlewood 21
Maximal function, Peetre — Fefferman — Stein 22
Maximum principle 137 441 456
Means of differences 84
Minkowski content 50
Minkowski dimension, upper 49
Mollification 305
Multiplication algebra 221
Nikol'skij representation 58
Normal form, cusp point 485
Normal form, fold point 482
Operator, analytic 262
Operator, bounded 261 413 414 428
Operator, coercive 393 487
Operator, completely continuous 262 399
Operator, composition 267
| Operator, composition, analycity 382
Operator, composition, continuity 374
Operator, composition, local Lipschitz continuity 372
Operator, composition, Taylor formula 381
Operator, compositon, Frechet-differentiability 378
Operator, continuous 261
Operator, dilation 15
Operator, extension 76
Operator, formal adjoint 131
Operator, Frechet-differentiable 262
Operator, Fredholm 129 134
Operator, Fredholm, nonlinear 473
Operator, identity 18
Operator, Laplace 10 18
Operator, lifting 76
Operator, Lipschitz continuous 261
Operator, locally Lipschitz continuous 262
Operator, monotone 393 457
Operator, Nemytskij 264 383
Operator, Nemytskij, boundedness 387
Operator, Nemytskij, continuity 389
Operator, nonlinear 87 261
Operator, of finite rank 129
Operator, properly elliptic 100
Operator, pseudodifferential 385
Operator, restriction 75
Operator, right inverse 133 136
Operator, sublinear 413 416 436
Operator, superlinear 413 419
Operator, trace 75
Operator, uniform continuous 261
Operator, with linear growth 413 418 439
Paraproduct 165
Perimeter 52
Perimeter, locally finite 215
Point, 1 — 1-transverse 483
Point, 1-transverse 481
Point, critical 471
Point, cusp 484 506 509 512
Point, fold 482 506 507
Point, regular 471
Point, singular 471 474 505
Poisson integral 113
Product of distributions 144 149 164 256 257
Quasi-norm 5
Resolution of unity 8
Retraction 75
Singular set 471 506
Space, admissible 400 412 451
Space, anisotropic 10
Space, Banach 9
Space, Besov 8 13
Space, Bessel-potential 13
Space, BMO 13
Space, bounded mean oscillation 228
Space, dual 19 84
Space, dual rich 126 424 469 472 473 489
Space, factor 125 472
Space, Hardy 13
Space, Hoelder 12
Space, homogeneous 94
Space, John — Nirenberg 227
Space, Lebesgue 11
Space, Lipschitz 13
Space, mixed dominated smoothness 10
Space, periodic 10
Space, positive cone 284 361
Space, quasi-Banach 5 9
Space, real-valued part 291
Space, Schwartz 6
Space, Slobodeckij 12
Space, Sobolev 12
Space, Sobolev, fractional order 13
Space, subcritical 267
Space, supercritical 267
Space, Triebel — Lizorkin 8
Space, weighted 10
Space, Zygmund 12
Spectral result 409
Subsolution 453 513
Supersolution 453 513
System, complemented 101
System, normal 101
System, regular 102
System, regular elliptic 99
Theorem, division, infinite-dimensional 477
Theorem, division, Mather 476
Theorem, division, Weierstrass 476
Theorem, Fubini-type 70
Theorem, implicit function 471
Theorem, inverse image 480
Theorem, Kazdan — Warner 452
Theorem, Liouville 118
Theorem, Paley — Wiener — Schwartz 80
Theorem, preparation, Malgrange 476 478
Theorem, preparation, Weierstrass 476
Theorem, Sard 489
Theorem, Sard — Smale 489
Wavelets 62
Withney type decomposition 217
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