Weighted gradient estimates for the parabolic pp-Laplacian equations

In this paper we obtain the weighted LqLq estimates of the gradients of weak solutions for the quasilinear parabolic equations of pp-Laplacian type with small BMO coefficients. For every ε∈(0,q−1)ε∈(0,q−1) if |∇u|p∈Lw,loc1+ε(ΩT) and |f|p∈Lw,locq(ΩT), then we prove that |∇u|p∈Lw,locq(ΩT). Our results improve the known results for such equations using a harmonic analysis free technique.