Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5773480 | Annales de l'Institut Henri Poincare (C) Non Linear Analysis | 2017 | 26 Pages |
Abstract
In this paper we establish the existence of Lipschitz-continuous solutions to the Cauchy Dirichlet problem of evolutionary partial differential equations{âtuâdivDf(Du)=0in ΩT,u=uoon âPΩT. The only assumptions needed are the convexity of the generating function f:RnâR, and the classical bounded slope condition on the initial and the lateral boundary datum uoâW1,â(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 âΩ, and the boundary may contain flat parts, for instance Ω could be a rectangle in Rn.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Verena Bögelein, Frank Duzaar, Paolo Marcellini, Stefano Signoriello,