Weak Harnack estimates for supersolutions to doubly degenerate parabolic equations

Qifan Li

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arXiv · 1711.00061

Weak Harnack estimates for supersolutions to doubly degenerate parabolic equations

Qifan Li

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Abstract

We establish weak Harnack inequalities for positive, weak supersolutions to certain doubly degenerate parabolic equations. The prototype of this kind of equations is $$\partial_tu-\operatorname{div}|u|^{m-1}|Du|^{p-2}Du=0,\quad p>2,\quad m+p>3.$$ Our proof is based on Caccioppoli inequalities, De Giorgi's estimates and Moser's iterative method.

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Qifan Li. 2017-10-31. Weak Harnack estimates for supersolutions to doubly degenerate parabolic equations. https://arxiv.org/abs/1711.00061

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