Maximal regularity for gradient systems with boundary degeneracy

Abstract

We study a class of elliptic operators L that degenerate at the boundary of a bounded open set O ⊂ R d and possess a symmetrizing invariant measure µ. Such operators are associated with diffusion processes in O which are invariant for time reversal. After showing that the corresponding elliptic equation λϕ − Lϕ = f has a unique weak solution for any λ > 0 and f ∈ L 2 (O, µ), we obtain new results for the characterization of the domain of L.