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Zeitschrift für Analysis und ihre Anwendungen

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Volume 34, Issue 2, 2015, pp. 165–174
DOI: 10.4171/ZAA/1534

Published online: 2015-04-08

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

Jun Zheng[1], Binhua Feng[2] and Zhihua Zhang[3]

(1) Southwest Jiatong University, Emeishan, Sichuan, China
(2) Northwest Normal University, Lanzhou (Gansu), China
(3) University of Electronic Science and Technology, Chengdu, Sichuan, China

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.

Keywords: $G$-Laplacian, Radon measure, Hölder continuity, regularity

Zheng Jun, Feng Binhua, Zhang Zhihua: Regularity of Solutions to the $G$-Laplace Equation Involving Measures. Z. Anal. Anwend. 34 (2015), 165-174. doi: 10.4171/ZAA/1534