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arXiv · 1004.3046

Gradient estimates for degenerate quasi-linear parabolic equations

Vitali Liskevich·Igor I. Skrypnik·Zeev Sobol
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Abstract

For a general class of divergence type quasi-linear degenerate parabolic equations with differentiable structure and lower order coefficients form bounded with respect to the Laplacian we obtain $L^q$-estimates for the gradients of solutions, and for the lower order coefficients from a Kato-type class we show that the solutions are Lipschitz continuous with respect to the space variable.

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Vitali Liskevich, Igor I. Skrypnik, Zeev Sobol. 2010-10-08. Gradient estimates for degenerate quasi-linear parabolic equations. https://doi.org/10.1112/jlms%2Fjdr020

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