Gradient continuity estimates for elliptic equations of singular p-Laplace type with measure data

2025/07/20 by Xu, Longjuan, Zhao, Yirui
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2507.15029

Abstract

In this paper, we are concerned with elliptic equations of p-Laplace type with measure data, which is given by -div(a(x)(|∇ u|²+s²)^(p-2)/(2)∇ u)=μ with p>1 and s≥0. Under the assumption that the modulus of continuity of the coefficient a(x) in the L²-mean sense satisfies the Dini condition, we prove a new comparison estimate and use it to derive interior and global gradient pointwise estimates by Wolff potential for p≥ 2 and Riesz potential for 1

Citations

• Pointwise gradient estimates for a class of singular quasilinear\n equation with measure data
• Good-λ and Muckenhoupt-Wheeden type bounds in quasilinear measure datum problems, with applications
• Gradient estimates for Stokes systems in domains
• A nonlinear Stein theorem
• Universal potential estimates
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Related

• Gradient estimates for singular p-Laplace type equations with measure data
• Gradient estimates for singular quasilinear elliptic equations with measure data
• Global gradient estimates for very singular quasilinear elliptic equations with measure data
• Gradient estimates for singular parabolic p-Laplace type equations with measure data
• Pointwise gradient estimates for a class of singular quasilinear\n equation with measure data