Hölder estimates for parabolic operators on domains with rough boundary

Abstract

In this paper we investigate linear parabolic, second-order boundaryvalue problems with mixed boundary conditions on rough domains. Assuming only boundedness/ellipticity on the coefficient function and very mild conditions on the geometry of the domain – including a very weak compatibility condition between the Dirichlet boundary part and its complement – we prove H¨older continuity of the solution in space and time