In this paper, we prove well-posedness and smoothness results in anisotropic Sobolev spaces for the solutions of boundary value problems with Dirichlet-Robin type boundary conditions for second-order parabolic equations in non-rectangular domains.Mathematics Subject Classification. 35K05, 35K20.

Abstract. In this work we give new results of existence , uniqueness and maximal regularity of a solution to a parabolic equation set in a nonregular domain Q with Cauchy-Dirichlet boundary conditions, wherewith some assumptions on the functions ( ϕ i ) i=1,2 . The right-hand side term of the equation is taken in L 2 (Q) . The method used is based on the approximation of the domain Q by a sequence of subdomains (Q n ) n which can be transformed into regular domains . This work is an extension of the one space variable case studied in [12].Mathematics subject classification (2010): 35K05, 35K20.

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This paper is devoted to the analysis of the N‐space dimensional heat equation, subject to Cauchy–Dirichlet boundary conditions. The problem is set in a symmetric conical type domain. More precisely, we look for sufficient conditions on the lateral boundary of the domain, as weak as possible in order to obtain the maximal regularity of the solution in an anisotropic Hilbertian Sobolev space. For this purpose, the domain decomposition method is employed. Copyright © 2013 John Wiley & Sons, Ltd.