Regularity of Solutions to the $G$-Laplace Equation Involving Measures

Jun Zheng; Binhua Feng; Zhihua Zhang

doi:10.4171/zaa/1534

JournalszaaVol. 34, No. 2pp. 165–174

Regularity of Solutions to the $G$ -Laplace Equation Involving Measures

Jun Zheng
Southwest Jiatong University, Emeishan, Sichuan, China
MathSciNet zbMATH Open
Binhua Feng
Northwest Normal University, Lanzhou (Gansu), China
MathSciNet zbMATH Open
Zhihua Zhang
University of Electronic Science and Technology, Chengdu, Sichuan, China
MathSciNet zbMATH Open

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Abstract

We establish regularity of solutions to the equation $- Δ_{G} u = μ$ , provided that $μ (B_{r} (x_{0})) \leq C r^{β}$ for any ball $B_{r} (x_{0}) \subset Ω$ with $r \leq 1$ , where $β > 0$ and $G$ satisfies certain structural conditions.

Cite this article

Jun Zheng, Binhua Feng, Zhihua Zhang, Regularity of Solutions to the $G$ -Laplace Equation Involving Measures. Z. Anal. Anwend. 34 (2015), no. 2, pp. 165–174

DOI 10.4171/ZAA/1534