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arXiv · 1912.10075

Gradient regularity for a singular parabolic equation in non-divergence form

Amal Attouchi·Eero Ruosteenoja
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Abstract

In this paper we consider viscosity solutions of a class of non-homogeneous singular parabolic equations $$\partial_t u-|Du|^\gamma\Delta_p^N u=f,$$ where $-1<\gamma<0$, $1<p<\infty$, and $f$ is a given bounded function. We establish interior H\"older regularity of the gradient by studying two alternatives: The first alternative uses an iteration which is based on an approximation lemma. In the second alternative we use a small perturbation argument.

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Amal Attouchi, Eero Ruosteenoja. 2019-12-20. Gradient regularity for a singular parabolic equation in non-divergence form. https://arxiv.org/abs/1912.10075

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