Abstract
The purpose of this article is to establish the well posedness and the regularity of the solution of the initial boundary value problem with Dirichlet boundary conditions for second-order parabolic systems in cylinders with polyhedral base.
Highlights
Boundary value problems for partial differential equations and systems in nonsmooth domains have been attracted attentions of many mathematicians for more than last 50 years
We are concerned with initial boundary value problems (IBVP) for parabolic equations and systems in nonsmooth domains
We apply the results for elliptic boundary value problems in polyhedral domains given in [4,5] and former our results to deal with the global regularity of the solution
Summary
Boundary value problems for partial differential equations and systems in nonsmooth domains have been attracted attentions of many mathematicians for more than last 50 years. We are concerned with initial boundary value problems (IBVP) for parabolic equations and systems in nonsmooth domains. These problems in cylinders with bases containing conical points have been investigated in [1,2] in which the regularity and the asymptotic behaviour near conical points of the solutions are established. For a vector-valued function u = (u1, u2, ..., us) and p = (p1, p2, ..., pn) Î Nn we use the notation Dpu = We denote by Hm,k(QT, g) (g Î R) the weighed Sobolev space of vector-valued functions u defined in QT with the norm. For a Î R, we denote by Ham( ) the weighed Sobolev space of vector functions u defined on Ω with the norm
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