Elliptic operators with unbounded diffusion coefficients in L2 spaces with respect to invariant measures

Abstract

We study the self-adjoint and dissipative realization A of a second order elliptic differential operator \({\user1{\mathcal{A}}}\) with unbounded regular coefficients in \(L^{2} ({\user2{\mathbb{R}}}^{N} ,\mu )\), where μ(dx) = ρ (x)dx is the associated invariant measure. We prove a maximal regularity result under suitable assumptions, that generalize the well known conditions in the case of constant diffusion part.