Maximal \(L^2\) regularity for Dirichlet problems in Hilbert spaces

DOI10.1016/j.matpur.2012.10.008zbMath1293.35359arXiv1201.3809OpenAlexW2016315745MaRDI QIDQ387985

Alessandra Lunardi, Giuseppe Da Prato

Publication date: 18 December 2013

Published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1201.3809

zbMATH Keywords

Dirichlet problemsfinite-dimensional approximationmaximal Sobolev regularitycylindrical functionsOrnstein-Uhlenbeck operatorsPDEs in infinite dimensions

Mathematics Subject Classification ID

PDEs on infinite-dimensional (e.g., function) spaces (= PDEs in infinitely many variables) (35R15)

Related Items (10)

Maximal \(L^{2}\) regularity for Ornstein-Uhlenbeck equation in convex sets of Banach spaces ⋮ Capacities, removable sets and \(L^p\)-uniqueness on Wiener spaces ⋮ Strong uniqueness for stochastic evolution equations in Hilbert spaces perturbed by a bounded measurable drift ⋮ \(L ^{2}\)-theory for non-symmetric Ornstein-Uhlenbeck semigroups on domains ⋮ Characterizations of Sobolev spaces on sublevel sets in abstract Wiener spaces ⋮ Traces of Sobolev functions on regular surfaces in infinite dimensions ⋮ Sobolev functions on infinite-dimensional domains ⋮ \(BV\) functions on open domains: the Wiener case and a Fomin differentiable case ⋮ On functions of bounded variation on convex domains in Hilbert spaces ⋮ Schauder theorems for a class of (pseudo‐)differential operators on finite‐ and infinite‐dimensional state spaces

Cites Work

• On the Dirichlet semigroup for Ornstein-Uhlenbeck operators in subsets of Hilbert spaces
• Kolmogorov equation associated to the stochastic reflection problem on a smooth convex set of a Hilbert space. II.
• Boundedness of Riesz transforms for elliptic operators on abstract Wiener spaces
• Kolmogorov equation associated to the stochastic reflection problem on a smooth convex set of a Hilbert space
• Symmetric Ornstein-Uhlenbeck semigroups and their generators
• Sobolev spaces over the Wiener space based on an Ornstein-Uhlenbeck operator
• \(L^p\)-regularity for elliptic operators with unbounded coefficients
• 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
• Stochastic Equations in Infinite Dimensions
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