Regularity for Fully Nonlinear P-Laplacian Parabolic Systems: the Degenerate Case

Le, Dung

Adv. Nonlinear Stud. 14 (2014), no. 1, 199–237

This paper introduces new nonlinear heat approximation and L∞ preserving homotopy techniques to investigate regularity properties of bounded weak solutions of strongly coupled p-Laplacian parabolic systems which consist of more than one equation defined on a domain of any dimension. The main results imply everywhere Holder continuity of bounded weak solutions and the global existence of strong solutions to nonlinear p-Laplacian systems.