Study of the first boundary value problem for a fourth order parabolic equation in a nonregular domain of

Abstract

This paper is concerned with the extension of solvability results obtained for a fourth order parabolic equation, set in a nonregular domain of R3 obtained in [1], to the case where the domain is cylindrical, not with respect to the time variable, but with respect to N space variables, N > 1. More precisely, we determine optimal conditions on the shape of the boundary of a (N + 1)-dimensional domain, N > 1, under which the solution is regular.