Global gradient estimates for degenerate parabolic equations in nonsmooth domains

摘要

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 the gradient. The results extend to the parabolic systems as well. The higher integrability estimates provide a useful tool in several applications.