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Acta Mathematica Vietnamica

Lp-Regularity for the Cauchy-Dirichlet Problem for Parabolic Equations in Convex Polyhedral Domains

icon-email Vu Trong Luong , Nguyen Thanh Anh , Do Van Loi

Abstract

In this paper, we study the regularity of the solution of the initial-boundary value problem with Dirichlet boundary conditions for second-order divergence parabolic equations in a domain of polyhedral type. We establish several results on the regularity of the solution in weighted Lp-Sobolev spaces.