Local Holder regularity for the general non-homogeneous parabolic equations

In this paper we obtain the local Holder regularity estimates of the gradient of weak solutions for the following general non-homogeneous parabolic equations with the logarithmic term in divergence form u(t) - div ((ADu center dot Du)(p-2/2) ln (e + (ADu center dot Du)(1/2)) ADu) = div (|f|(p-2) ln (e + |f|)) in Omega(T), where Omega(T) := Omega x (0, T) with T > 0 and Omega is an open bounded domain in R-n, under some proper conditions on A and f. We would like to point out that our result in the present work is a generalized version of the known results for the classical parabolic p-Laplacian equation without the logarithmic term. (c) 2022 Elsevier Inc. All rights reserved.