Gradient estimates for degenerate quasi-linear parabolic equations

Details Gradient estimates for degenerate quasi-linear parabolic equations Gradient estimates for degenerate quasi-linear parabolic equations

2010-04-18

arxiv.org/abs/1004.3046v2

Mathematics

Analysis of PDEs

Scientific paper

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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