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 [Formula: see text]-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 [Formula: see text]-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.