Article ID Journal Published Year Pages File Type
5773480 Annales de l'Institut Henri Poincare (C) Non Linear Analysis 2017 26 Pages PDF
Abstract
In this paper we establish the existence of Lipschitz-continuous solutions to the Cauchy Dirichlet problem of evolutionary partial differential equations{∂tu−divDf(Du)=0in ΩT,u=uoon ∂PΩT. The only assumptions needed are the convexity of the generating function f:Rn→R, and the classical bounded slope condition on the initial and the lateral boundary datum uo∈W1,∞(Ω). We emphasize that no growth conditions are assumed on f and that - an example which does not enter in the elliptic case - uo could be any Lipschitz initial and boundary datum, vanishing at the boundary ∂Ω, and the boundary may contain flat parts, for instance Ω could be a rectangle in Rn.
Related Topics
Physical Sciences and Engineering Mathematics Analysis
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