Abstract
A partial regularity theorem is established for weak solutions of elliptic equations of the form $\mbox{div}(A(y)\nabla\psi)=0$. Here we allow the possibility that the eigenvalues of $A(y)$ are not bounded away from $0$ below. This result is then used to prove an everywhere regularity theorem for weak solutions of the initial- boundary-value problem for the system $\frac{\partial u}{\partial t}-\Delta u = \sigma(u)|\nabla \varphi|^2$, $\mbox{div}(\sigma(u) \nabla\varphi)=0$ in the case where $\sigma$ may decay exponentially.
Citation
Xiangsheng Xu. "A local partial regularity theorem for weak solutions of degenerate elliptic equations and its application to the thermistor problem." Differential Integral Equations 12 (1) 83 - 100, 1999. https://doi.org/10.57262/die/1367266995
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