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 R 3 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

Keywords

• Fourth order parabolic equations,Nonregular domains,Anisotropic weightedSobolev spaces

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