Gradient estimates for degenerate quasi-linear parabolic equations

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.

References in corpus (3)

• Local Lipschitz regularity for degenerate elliptic systems
• Infinitesimal form boundedness and Trudinger's subordination for the Schrödinger operator
• Potential estimates for quasi-linear parabolic equations

Cited by in corpus (2)

• Feller evolution families and parabolic equations with form-bounded vector fields
• Fujita type results for quasilinear parabolic inequalities with nonlocal terms