Local regularity for quasi-linear parabolic equations in non-divergence form

Amal Attouchi

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arXiv · 1809.03241

Local regularity for quasi-linear parabolic equations in non-divergence form

Amal Attouchi

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Abstract

We consider viscosity solutions to non-homogeneous degenerate and singular parabolic equations of the $p$-Laplacian type and in non-divergence form. We provide local H\"older and Lipschitz estimates for the solutions. In the degenerate case, we prove the H\"older regularity of the gradient. Our study is based on a combination of the method of alternatives and the improvement of flatness estimates.

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Amal Attouchi. 2018-09-10. Local regularity for quasi-linear parabolic equations in non-divergence form. https://arxiv.org/abs/1809.03241

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