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Cerrai S. — Second Order PDEs in Finite and Infinite Dimension
Cerrai S. — Second Order PDEs in Finite and Infinite Dimension



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Название: Second Order PDEs in Finite and Infinite Dimension

Автор: Cerrai S.

Язык: en

Рубрика: Математика/Вероятность/Стохастические процессы/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2001

Количество страниц: 330

Добавлена в каталог: 29.10.2004

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$(X,Y)_{\theta,\infty}$, interpolation space      17
$B_{b}(X;Y)$      15
$C(\bar{\mathcal{O}};\mathbb{R}^{n})$      15
$C^{\theta}(\bar{\mathcal{O}};\mathbb{R}^{n})$ $\theta$-Hoelder continuous functions      15
$C^{\theta}_{b}(X;Y)$, $\theta$-Hoelder continuous functions      16
$C_{b}(X;Y)$, $C_{b}^{k}(X;Y)$, $k\geq1$      15
$C_{b}^{0,1}(X;Y)$, $C_{b}^{k,1}(X;Y)$, $k\geq1$, Lipschitz continuous functions      16
$K^{r,p}_{q}(T,H)$, $K^{p}_{q}(T,H)$      18
$L^{p}(\mathcal{O};\mathbb{R}^n)$      14
$W^{s,p}(\mathcal{O};\mathbb{R}^{n})$      15
$\mathcal{C}^{\alpha}_{b}(X;Y)$, Zygmund space      16
$\mathcal{C}_p(T,X)$      113 186
$\mathcal{H}_{2}(T,\mathbb{R}^{d})$, $\mathcal{H}_{p}(T,X)$      27 113
$\mathcal{L}(X;Y)$, $\mathcal{L}(X)$ (if $X=Y$), bounded linear operators      14
$\mathcal{L}^{+}(X)$,cfr. symmetric non-negative operators      14
$\mathcal{L}_{1}(X)$cfr. trace class operator      14
$\mathcal{L}_{2}(X)$cfr. Hilbert — Schmidt operator      14
Absolutely continuous measure      77
Adapted control      282
Admissible control      13 293
Analytic semigroup      82 100 107 174
Approximate controllability      66
Associated control system      237
Banach spaces-valued stochastic system      171
Bismut — Elworthy formula      3 7 48 82 172 206
Bismut — Elworthy formula, generalized Bismut — Elworthy formula      9
Chapman — Kolmogorov law      68 130
Classical solutions      52 154
Closed loop equation      12 282 286 292
Comparison theorems      6
Conormal boundary condition      173
Contractions depending on parameters theorem      313
Controlled state system      239 281
Cost functional,      2 281 289
Cylindrical Wiener process      110
Degenerate elliptic operator      81
Dependence on data      105
Dependence on data, differential dependence      34 113
Differentiability in the mean of order $p$      114 118 121
Differentiability, mean-square differentiability      82 91 114
Dirichlet boundary condition      108 173
Dissipative mapping      303
Doob theorem      4 10 66 222 229
Ergodic measure      68
Euler solvability      1
Exponentially mixing measure      4 68
Factorization method      156
Feedback formula      297
Feller property      67 130
Feller semigroup      106 200 209
Fractional power of operators      110
Galerkin approximation      238
Generalized solution      9 207 211 239
Giuzburg — Landau equation      6
Hamilton — Jacobi — Bellman equation      10 237
Hamilton — Jacobi — Bellman equation, elliptic HJB equation      267
Hamilton — Jacobi — Bellman equation, porabolic HJB equation      253
Hilbert — Schmidt operator      14
Hille — Yosida theorem      308
Infinitesimal generator      209 306
Interpolation theory      17
Interpolation theory, infinite dimensional interpolation      168
Interpolation theory, interpolation space      56
Interpolation theory, interpolation theorem      56
Invariant measure,      66
Irreducibility      4 66 73 222 229
Ito's formula      27 passim
K-convergence      305
Khas'minskii theorem      4 10 66 70 222 229
Krylov — Bogoliubov theorem      10 69 221
Legendre transform      12 281
m-dissipative operator      274
Markov semigroup      21 200 205
Markov transition probabilities family      67
Martingale solution      13 283
Maximal martingale inequalities      27 31
Mild solution      186 207 239
Nemytskii operator      112
Oblique boundary condition      108
Operator of negative type      109
Optimal control      284 282 287 292 297
Optimal regularity in Hoelder spaces      2
Optimal state      285 283 287 292 297
Ornstein — Uhlenbeck system      81 111 176
Predictable $\sigma$-algebra      27
Predictable process      27
Prohorov theorem      69 132
Pseudo-inverse      107
Pseudo-resolvent      307
Rate of convergence to equilibrium      4 68
Rate, exponential convergence      66 79
Rate, polynomial convergence      77
Reaction-diffusion system      6 107
Relaxed control      282
Schauder estimates      2 7 21 56 61 144 168
Stochastic control problem      281
Stochastic convolution      110
Stochastic Fubini — Tonelli theorem      156
Strict solution      53 155 165
Strong Feller property      4 66 172 209 222 229
Strong Law of Large Numbers      221
Strong solution      165 187
Strongly mixing measure      4 68
Subdifferential      301
Subdifferential of the norm      303
Symmetric non-negative operator      14
Tight set of measures      47 69 221
Total variation convergence      70
Trace-class operator      14
Ultracontractive semigroup      106 112
Value function      12 281 289
Variation equation      34
Variation equation, first Variation equation      37 114 191 211 246
Variation equation, second Variation equation      39
Variation of constants formula      11 60
Variation, higher ordervariation equation      43 127 134 191
Ventcel's boundary condition      5
Verification theorem      10 282
Weak convergence      69
Weakly continuous semigroups      22 130 305
Weakly continuous, weak generator      55 308
Yosida approximation      159 303
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