Linear parabolic equations with strong boundary degeneration

Abstract

As an application of the theory of linear parabolic differential equations on noncompact Riemannian manifolds, developed in earlier papers, we prove a maximal regularity theorem for nonuniformly parabolic boundary value problems in Euclidean spaces. The new feature of our result is the fact that-besides of obtaining an optimal solution theory-we consider the 'natural' case where the degeneration occurs only in the normal direction.2010 Mathematics Subject Classification. 35K65 35K45 53C44 Key words and phrases: Degenerate parabolic boundary value problems, Riemannian manifolds with bounded geometry.