Sharp regularity for the degenerate doubly nonlinear parabolic equation

Abstract

The aim of this paper is to provide sharp regularity estimates for locally bounded solutions of the degenerate doubly nonlinear parabolic equationut−div(m|u|m−1|Du|p−2Du)=f, where m>1, p>2 and f∈Lq,r. More precisely, we show that solutions are locally of class C0,β, where β depends explicitly only on the optimal Hölder exponent for solutions of the homogeneous case, the integrability of f in space and time, and the nonlinearity parameters p and m.