Maximal Sobolev regularity for solutions of elliptic equations in infinite dimensional Banach spaces endowed with a weighted Gaussian measure
Let $X$ be a separable Banach space endowed with a non-degenerate centered Gaussian measure $μ$. The associated Cameron-Martin space is denoted by $H$. Let $ν=e^{-U}μ$, where $e^{-U}$ is a sufficiently regular weight and $U:X\rightarrow\mathbb{R}$ 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 $λ>0$, $f\in L^2(X,ν)$ and $L_ν$ is the self-adjoint operator associated with the quadratic form \[(ψ,φ)\mapsto \int_X\left\langle\nabla_Hψ,\nabla_Hφ\right\rangle_Hdν\qquadψ,φ\in W^{1,2}(X,ν).\]
math.AP↗