Calderón-Zygmund estimates for a class of quasilinear parabolic equations

In this paper we obtain the following local Calderón-Zygmundestimates Gf∈Llocq(ΩT)⇒G∇u∈Llocq(ΩT)for anyq≥1of weak solutions for a class of quasilinear parabolic equations ut−diva∇u∇u=divaffinΩT,where G(t)=∫0tτa(τ)dτ for t≥0. We remark that G(t)=|t|plog(1+|t|)forp>2satisfies the given conditions in this work. Moreover, we would like to point out that our results improve the known results for such equations.