CPAA
The obstacle problem for Monge-Ampère type equations in non-convex domains
Jingang Xiong Jiguang Bao
Communications on Pure & Applied Analysis 2011, 10(1): 59-68 doi: 10.3934/cpaa.2011.10.59
In this paper, we consider the obstacle problem for Monge-Ampère type equations which include prescribed Gauss curvature equation as a special case. We establish $C^{1,1}$ regularity of the greatest viscosity solution in non-convex domains.
keywords: non-convex domain. Monge-Ampère equation Obstacle problem
DCDS
A Harnack inequality for fractional Laplace equations with lower order terms
Jinggang Tan Jingang Xiong
Discrete & Continuous Dynamical Systems - A 2011, 31(3): 975-983 doi: 10.3934/dcds.2011.31.975
We establish a Harnack inequality of fractional Laplace equations without imposing sign condition on the coefficient of zero order term via the Moser's iteration and John-Nirenberg inequality.
keywords: Harnack inequality Moser's iteration. Fractional Laplace equations

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