Weighted gradient estimates for the parabolic p-Laplacian equations. (January 2015) - Yao, Fengping
Abstract: In this paper we obtain the weighted L q estimates of the gradients of weak solutions for the quasilinear parabolic equations of p -Laplacian type with small BMO coefficients. For every ε ∈ ( 0, q − 1 ) if | ∇ u | p ∈ L w, l o c 1 + ε ( Ω T ) and | f | p ∈ L w, l o c q ( Ω T ), then we prove that | ∇ u | p ∈ L w, l o c q ( Ω T ) . Our results improve the known results for such equations using a harmonic analysis free technique.