A weighted Sobolev regularity theory of the parabolic equations with measurable coefficients on conic domains in R-d

Abstract

We establish existence, uniqueness, and arbitrary order Sobolev regularity results for the second order parabolic equations with measurable coefficients defined on the conic domains D of the type D(M) := {x is an element of Rd : x/vertical bar x vertical bar is an element of M } , M subset of Sd-1. We obtain the regularity results by using a system of mixed weights consisting of appropriate powers of the distance to the vertex and of the distance to the boundary. We also provide the sharp ranges of admissible powers of the distance to the vertex and to the boundary. (C) 2021 Elsevier Inc. All rights reserved.