Science China Mathematics

, Volume 62, Issue 11, pp 2073–2088 | Cite as

Some new estimates for the complex Monge-Ampère equation

  • Xiuxiong ChenEmail author
  • Jingrui Cheng


In this paper, we consider the complex Monge-Ampère equation posed on a compact Kahler manifold. We show how to get Lp (p < ∞) and L estimates for the gradient of the solution in terms of the continuity of the right-hand side.


complex Monge-Ampère equations gradient estimates Kähler manifold 


35R01 32W20 



This work was supported by National Science Foundation of USA (Grant No. DMS-1914719).


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Copyright information

© Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsSUNY Stony BrookStony BrookUSA
  2. 2.Simons Center for Geometry and PhysicsSUNY Stony BrookStony BrookUSA

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