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

### Jun Zheng

Southwest Jiatong University, Emeishan, Sichuan, China### Binhua Feng

Northwest Normal University, Lanzhou (Gansu), China### Zhihua Zhang

University of Electronic Science and Technology, Chengdu, Sichuan, China

## Abstract

We establish regularity of solutions to the equation $-\Delta_{G}u= \mu$, provided that $\mu (B_{r}(x_{0}))\leq Cr^{\beta}$ for any ball $B_{r}(x_{0})\subset \Omega$ with $r\leq 1$, where $\beta>0$ 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