Weighted gradient estimates for the parabolic p-Laplacian equations. (January 2015)

• Record Type: Journal Article
• Authors: Yao, Fengping
• Is Part Of: Nonlinear analysis. Volume 112(2015)
• Page Start: 58
• Page End: 68
• Publication Date: 2015-01
• Subjects: 35K55 -- 35K65; Lq estimates -- Weighted -- Regularity -- Gradient -- Divergence -- Parabolic -- p-Laplacian; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2014.09.010
• Languages: English
• ISSNs: 0362-546X

Abstract

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.