End point gradient estimates for quasilinear parabolic equations with variable exponent growth on nonsmooth domains

Global gradient estimates for degenerate parabolic equations in nonsmooth domains

Abstract. This paper studies the global regularity theory for degenerate nonlinear parabolic partial differential equations. Our objective is to show that weak solutions belong to a higher Sobolev space than assumed a priori if the complement of the domain satisfies a capacity density condition and if the boundary values are sufficiently smooth. Moreover, we derive integrability estimates for t...

Anisotropic quasilinear elliptic equations with variable exponent

We study some anisotropic boundary value problems involving variable exponent growth conditions and we establish the existence and multiplicity of weak solutions by using as main argument critical point theory. 2000 Mathematics Subject Classification: 35J60, 35J62, 35J70.

A priori estimates for quasilinear degenerate parabolic equations

We prove some maximum and gradient estimates for classical solutions to a wide class of quasilinear degenerate parabolic equations, including first order ones. The proof is elementary and exploits the smallness of the domain in the time direction.

Research Article Interior Gradient Estimates for Nonuniformly Parabolic Equations II

Gradient estimates for degenerate quasi-linear parabolic equations

For a general class of divergence type quasi-linear degenerate parabolic equations with differentiable structure and lower order coefficients infinitesimally form bounded with respect to the Laplacian we obtain Lq-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 var...