Partial regularity for degenerate parabolic systems with non-standard growth and discontinuous coefficients

Qifan Li

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arXiv · 2202.05051

Partial regularity for degenerate parabolic systems with non-standard growth and discontinuous coefficients

Qifan Li

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Abstract

This article studies the partial H\"older continuity of weak solutions to certain degenerate parabolic systems whose model is the differentiable parabolic $p(x,t)$-Laplacian system, \begin{equation*}\partial_t u-\operatorname{div}[\mu(z)(1+|Du|^2)^{\frac{p(z)-2}{2}}Du]=0,\qquad p(z)\geq2.\end{equation*} Here, the exponential function $p(z)$ satisfies a logarithmic continuity condition. We show that if $\mu(z)$ satisfies a certain VMO-type condition, then $u$ is locally H\"older continuous except for a measure zero set.

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Qifan Li. 2022-02-10. Partial regularity for degenerate parabolic systems with non-standard growth and discontinuous coefficients. https://arxiv.org/abs/2202.05051

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