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$L_p$-Regularity for the Cauchy-Dirichlet Problem for Parabolic Equations in Convex Polyhedral Domains
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 $L_p$-Sobolev spaces.