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| Cerrai S. — Second Order PDEs in Finite and Infinite Dimension |
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| Предметный указатель |
 , interpolation space 17
 15
 15
  -Hoelder continuous functions 15
 , -Hoelder continuous functions 16
 ,  ,  15
 ,  , , Lipschitz continuous functions 16
 ,  18
 14
 15
 , Zygmund space 16
 113 186
 ,  27 113
 ,  (if  ), bounded linear operators 14
 ,cfr. symmetric non-negative operators 14
 cfr. trace class operator 14
 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  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  -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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