Continuity of solutions to the $G$-Laplace equation involving measures

Yan Zhang, Jun Zheng
2019 Electronic Journal of Qualitative Theory of Differential Equations  
We establish local continuity of solutions to the G-Laplace equation involving measures, i.e., where µ is a nonnegative Radon measure satisfying µ(B r (x 0 )) ≤ Cr m for any ball B r (x 0 ) ⊂⊂ Ω with r ≤ 1 and m > n − 1 − δ ≥ 0. The function g is supposed to be nonnegative and C 1 -continuous on [0, +∞), satisfying g(0) = 0 and δ ≤ tg (t) g(t) ≤ g 0 , ∀t > 0 with positive constants δ and g 0 , which generalizes the structural conditions of Ladyzhenskaya-Ural'tseva for an elliptic operator.
doi:10.14232/ejqtde.2019.1.39 fatcat:tpul23qp6bdebhibaaak3jfpr4