A new short proof of regularity for local weak solutions for a certain class of singular parabolic equations

Simone Ciani; Vincenzo Vespri

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arXiv · 2003.00746

A new short proof of regularity for local weak solutions for a certain class of singular parabolic equations

Simone Ciani·Vincenzo Vespri

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Abstract

We shall establish the interior H\"older continuity for locally bounded weak solutions to a class of parabolic singular equations whose prototypes are \begin{equation} u_t= \nabla \cdot \bigg( |\nabla u|^{p-2} \nabla u \bigg), \quad \text{ for } \quad 1 3-\frac{p}{N}, \end{equation} via a new and simplified proof using recent techniques on expansion of positivity and $L^{1}$-Harnack estimates.

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Simone Ciani, Vincenzo Vespri. 2020-03-02. A new short proof of regularity for local weak solutions for a certain class of singular parabolic equations. https://arxiv.org/abs/2003.00746

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