On the Dirichlet semigroup for Ornstein-Uhlenbeck operators in subsets of Hilbert spaces

DOI10.1016/j.jfa.2010.04.016zbMath1204.35172arXiv1006.1523OpenAlexW2078449262MaRDI QIDQ709225

Alessandra Lunardi, Giuseppe Da Prato

Publication date: 18 October 2010

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1006.1523

zbMATH Keywords

Sobolev spacesHilbert spacesGaussian measuresOrnstein-Uhlenbeck operatorsDirichlet semigroup

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Stochastic calculus of variations and the Malliavin calculus (60H07) Groups and semigroups of linear operators, their generalizations and applications (47D99) PDEs on infinite-dimensional (e.g., function) spaces (= PDEs in infinitely many variables) (35R15)

Related Items (9)

Capacities, removable sets and \(L^p\)-uniqueness on Wiener spaces ⋮ Maximal \(L^2\) regularity for Dirichlet problems in Hilbert spaces ⋮ \(L^2\)-theory for transition semigroups associated to dissipative systems ⋮ \(L ^{2}\)-theory for non-symmetric Ornstein-Uhlenbeck semigroups on domains ⋮ Surface measures in infinite dimension ⋮ Traces of Sobolev functions on regular surfaces in infinite dimensions ⋮ Sobolev functions on infinite-dimensional domains ⋮ Gradient estimates for perturbed Ornstein-Uhlenbeck semigroups on infinite-dimensional convex domains ⋮ Harnack inequalities with power \(\pmb{p\in (1,+\infty )}\) for transition semigroups in Hilbert spaces

Cites Work

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• Kolmogorov equation associated to the stochastic reflection problem on a smooth convex set of a Hilbert space
• An introduction to infinite-dimensional analysis
• An estimate of Burkholder type for stochastic processes defined by the stochastic integral
• A submartingale type inequality with applicatinos to stochastic evolution equations
• On the small balls problem for equivalent Gaussian measures
• Ornstein-Uhlenbeck semigroups in open sets of Hilbert spaces
• Dirichlet problem for parabolic equations on Hilbert spaces
• Dirichlet boundary conditions for elliptic operators with unbounded drift

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