Matzoh ball soup revisited: the boundary regularity issue

Rolando Magnanini, Shigeru Sakaguchi

We consider nonlinear diffusion equations of the form ${\partial }_{t}u=\Delta \varphi (u)$ in ${\mathbb{R}}^N$ with $N\ge 2.$ When $\varphi (s)\equiv s$, this is just the heat equation. Let $\Omega$ be a doma…