Sobolev spaces with respect to a weighted Gaussian measure in infinite dimensions

DOI10.1142/S0219025719500267zbMath1436.28010arXiv1510.08283OpenAlexW2999584271WikidataQ126579077 ScholiaQ126579077MaRDI QIDQ4960471

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Publication date: 16 April 2020

Published in: Infinite Dimensional Analysis, Quantum Probability and Related Topics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1510.08283

zbMATH Keywords

weighted Sobolev spacestracessublevel setsinfinite-dimensional analysisdivergence operatorweighted Gaussian measure

Mathematics Subject Classification ID

Measures and integration on abstract linear spaces (46G12) Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) (28C20)

Related Items (11)

Maximal \(L^{2}\) regularity for Ornstein-Uhlenbeck equation in convex sets of Banach spaces ⋮ BV functions in Hilbert spaces ⋮ Maximal Sobolev regularity for solutions of elliptic equations in Banach spaces endowed with a weighted Gaussian measure: the convex subset case ⋮ \(L^2\)-theory for transition semigroups associated to dissipative systems ⋮ Regularizing properties of (non-Gaussian) transition semigroups in Hilbert spaces ⋮ Domains of elliptic operators on sets in Wiener space ⋮ On the law of the minimum in a class of unidimensional SDEs ⋮ \(BV\) functions on open domains: the Wiener case and a Fomin differentiable case ⋮ On generators of transition semigroups associated to semilinear stochastic partial differential equations ⋮ On functions of bounded variation on convex domains in Hilbert spaces ⋮ On the domain of non-symmetric and, possibly, degenerate Ornstein-Uhlenbeck operators in separable Banach spaces

Cites Work

• Maximal Sobolev regularity for solutions of elliptic equations in infinite dimensional Banach spaces endowed with a weighted Gaussian measure
• Sobolev regularity for a class of second order elliptic PDE's in infinite dimension
• Random obstacle problems. École d'Été de Probabilités de Saint-Flour XLV -- 2015
• Kolmogorov equations for stochastic PDEs.
• Sets with finite perimeter in Wiener spaces, perimeter measure and boundary rectifiability
• Gaussian capacities
• Gaussian null sets and differentiability of Lipschitz map on Banach spaces
• Maximal Sobolev regularity for solutions of elliptic equations in Banach spaces endowed with a weighted Gaussian measure: the convex subset case
• Gradient estimates for perturbed Ornstein-Uhlenbeck semigroups on infinite-dimensional convex domains
• Traces of Sobolev functions on regular surfaces in infinite dimensions
• Domains of elliptic operators on sets in Wiener space
• Differentiability of Lipschitzian mappings between Banach spaces
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