Study of the First Boundary Value Problem for a Fourth Order Parabolic Equation in a Nonregular Domain of

Study of the First Boundary Value Problem for a Fourth Order Parabolic Equation in a Nonregular Domain of

A. Kheloufi

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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.

 

Keywords

Fourth order parabolic equations, Nonregular domains, Anisotropic weighted Sobolev spaces.