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Partial regularity of solutions to a class of degenerate systems

Authors:	Xiangsheng Xu

Institution:	Department of Mathematics and Statistics, Mississippi State University, Mississippi State, Mississippi 39762

Abstract:	We consider the system $\displaystyle \frac{\partial u }{\partial t}-\Delta u=\sigma \left ( u\right ) \left \| \nabla \varphi \right \| ^2$ , $\mathrm {div}\left ( \sigma \left ( u\right ) \nabla \varphi \right ) =0$ in $Q_T\equiv \Omega \times \left ( 0,T\right ]$ coupled with suitable initial-boundary conditions, where $\Omega$ is a bounded domain in $\mathbf {R}^N$ with smooth boundary and $\sigma \left ( u\right )$ is a continuous and positive function of . Our main result is that under some conditions on $\sigma$ there exists a relatively open subset of such that is locally Hölder continuous on , the interior of $Q_T\backslash Q_0$ is empty, and is essentially bounded on $Q_T\backslash Q_0$ .

Keywords:	Partial regularity degenerate systems

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