On the third boundary value problem for parabolic equations in a non-regular domain of RN+1

Abstract

In this paper, we look for sufficient conditions on the lateral surface of the domain and on the coefficients of the boundary conditions of a N?space dimensional linear parabolic equation, in order to obtain existence, uniqueness and maximal regularity of the solution in a Hilbertian anisotropic Sobolev space when the right hand side of the equation is in a Lebesgue space. This work is an extension of solvability results obtained for a second order parabolic equation, set in a non-regular 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.