Local Hölder regularity for the general non-homogeneous parabolic equations

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In this paper we obtain the local Hölder regularity estimates of the gradient of weak solutions for the following general non-homogeneous parabolic equations with the logarithmic term in divergence formut−div((ADu⋅Du)p−22ln⁡(e+(ADu⋅Du)12)ADu)=div(|f|p−2ln⁡(e+|f|)) in ΩT, where ΩT:=Ω×(0,T) with T>0 and Ω is an open bounded domain in Rn, 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.