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Estimates for viscosity solutions of parabolic equations with Dirichlet boundary conditions
Authors:G. Gripenberg
Affiliation:Institute of Mathematics, Helsinki University of Technology, P.O. Box 1100, FIN-02015 HUT, Finland
Abstract:It is shown how one can get upper bounds for $lvert u-v rvert$when $u$ and $v$ are the (viscosity) solutions of

begin{displaymath}u_t - alpha(D_x u) Delta_x u = 0quadtext{and}quad v_t - beta(D_x v) Delta_x v = 0, end{displaymath}

respectively, in $(0,infty)times Omega$ with Dirichlet boundary conditions. Similar results are obtained for some other parabolic equations as well, including certain equations in divergence form.

Keywords:Viscosity solution   parabolic   dependence on data   Dirichlet boundary condition
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