A Priori Estimate for the Complex Monge–Ampère Equation
Jiaxiang Wang , Xu-Jia Wang , Bin Zhou
Peking Mathematical Journal ›› 2020, Vol. 4 ›› Issue (1) : 143 -157.
A Priori Estimate for the Complex Monge–Ampère Equation
In this paper, we use the Sobolev type inequality in Wang et al. (Moser–Trudinger inequality for the complex Monge–Ampère equation, arXiv:2003.06056v1 (2020)) to establish the uniform estimate and the Hölder continuity for solutions to the complex Monge–Ampère equation with the right-hand side in $L^p$ for any given $p>1$. Our proof uses various PDE techniques but not the pluripotential theory.
ARC(DP 170100929)
NSFC(11822101)
China Scholarship Council(01906320165)
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