Maximal Sobolev regularity for solutions of elliptic equations in infinite dimensional Banach spaces endowed with a weighted Gaussian measure

Abstract

Let $X$ be a separable Banach space endowed with a non-degenerate centered Gaussian measure $\mu$. The associated Cameron-Martin space is denoted by $H$. Let $\nu =e^{-U}\mu$, where $e^{-U}$ is a sufficiently regular weight and $U:X\to \mathbb{R}$ is a convex and continuous function. In this paper we are interested in the $W^{2,2}$ regularity of the weak solutions of elliptic equations of the type \[λu-L_νu=f,\] where $\lambda >0$, $f\in L^2(X,\nu )$ and $L_{\nu }$ is the self-adjoint operator associated with the quadratic form \[(ψ,φ)\mapsto \int_X\left\langle\nabla_Hψ,\nabla_Hφ\right\rangle_Hdν\qquadψ,φ\in W^{1,2}(X,ν).\]

References in corpus (3)

• Maximal Sobolev regularity for solutions of elliptic equations in infinite dimensional Banach spaces endowed with a weighted Gaussian measure
• Maximal Sobolev regularity for solutions of elliptic equations in Banach spaces endowed with a weighted Gaussian measure: the convex subset case
• Sobolev spaces with respect to a weighted Gaussian measures in infinite dimensions

Cited by in corpus (11)

• Maximal Sobolev regularity for solutions of elliptic equations in infinite dimensional Banach spaces endowed with a weighted Gaussian measure
• Schauder theorems for a class of (pseudo-)differential operators on finite and infinite dimensional state spaces
• Maximal Sobolev regularity for solutions of elliptic equations in Banach spaces endowed with a weighted Gaussian measure: the convex subset case
• Regularizing properties of (non-Gaussian) transition semigroups in Hilbert spaces
• Gradient estimates for perturbed Ornstein-Uhlenbeck semigroups on infinite dimensional convex domains
• Sobolev spaces with respect to a weighted Gaussian measures in infinite dimensions
• On the domain of elliptic operators defined in subsets of Wiener spaces
• On functions of bounded variation on convex domains in Hilbert spaces
• Differentiability in infinite dimension and the Malliavin calculus
• Regarding the domain of non-symmetric and, possibly, degenerate Ornstein--Uhlenbeck operators in separable Banach spaces
• $L^2$-theory for transitions semigroups associated to dissipative systems