Parabolic p-Laplacian revisited : global regularity and fractional smoothness

Abstract

This paper presents an investigation on the existence, fractional and classical regularity in vector-valued Banach spaces for the solutions of a family of evolutive p-Laplacian-like equations subject to Neumann boundary conditions. Global space-time regularity to the solution and its time derivative in Nikolskii and Slobodeckii spaces is discussed and improved C-1-weak regularity for a class of intermediate dual spaces is obtained. Moreover, precise energy estimates showing the influence of the degeneracy pattern of the equation are provided