Regularity for solutions of the twophase Stefan problem
Marianne Korten  Department of Mathematics, Kansas State University, Manhattan, KS 66506, United States (email) Abstract: We consider the twophase Stefan problem $u_t=\Delta\alpha(u)$ where $\alpha(u) =u+1$ for $u<1$, $\alpha(u) =0$ for $1 \leq u \leq 1$, and $\alpha(u)=u1$ for $u \geq 1$. We show that if $u$ is an $L_{l o c}^2$ distributional solution then $\alpha(u)$ has $L_{l o c}^2$ derivatives in time and space. We also show $\alpha(u)$ is subcaloric and conclude that $\alpha(u)$ is continuous.
Keywords: Stefan problem, degenerate parabolic equation.
Received: March 2007; Revised: October 2007; Published: February 2008. 
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