## ON THE THIRD BOUNDARY VALUE PROBLEM FOR PARABOLIC EQUATIONS IN A NON-REGULAR DOMAIN OF RN+1

ON THE THIRD BOUNDARY VALUE PROBLEM FOR PARABOLIC EQUATIONS IN A NON-REGULAR DOMAIN OF RN+1

*AREZKI KHELOUFI*

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## Abstract

In this paper, we look for sucient conditions on the lateral surface of the domain and on the coecients of the boundary conditions of a Nspace 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 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:

## Keywords

Parabolic equations, Non-regular domains, Robin conditions, Anisotropic Sobolev spaces.