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Estimates of the second-order derivatives for solutions to the two-phase parabolic problem

By Darya Apushkinskaya and Nina Uraltseva

Abstract

The L_{\infty}-estimates of the second derivatives for solutions of the parabolic free boundary problem with two phases \Delta u-\partial_{t}u=\lambda^{+}\chi_{\left\{ u>0\right\} }-\lambda^{-}\chi_{\left\{ u<0\right\} }\textrm{in }B_{1}^{+}\times]-1,0],\textrm{ }\lambda^{\pm}\geq0,\lambda^{+}+\lambda^{-}>0, satisfying the non-zero Dirichlet condition on \Pi_{1}:=\left\{ (x,t):\left|x\right|\leq1,x_{1}=0,-1<t\leq0\right\}, are proved

Topics: Mathematics
Publisher: Fakultät 6 - Naturwissenschaftlich-Technische Fakultät I. Fachrichtung 6.1 - Mathematik
Year: 2008
OAI identifier: oai:scidok.sulb.uni-saarland.de:4755

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