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Hölder regularity for solutions to complex Monge–Ampère equations

Volume 113 / 2015

Mohamad Charabati Annales Polonici Mathematici 113 (2015), 109-127 MSC: Primary 32W20, 32U15; Secondary 35J96. DOI: 10.4064/ap113-2-1


We consider the Dirichlet problem for the complex Monge–Ampère equation in a bounded strongly hyperconvex Lipschitz domain in $\mathbb C^n$. We first give a sharp estimate on the modulus of continuity of the solution when the boundary data is continuous and the right hand side has a continuous density. Then we consider the case when the boundary value function is $\mathcal {C}^{1,1}$ and the right hand side has a density in $L^p(\varOmega )$ for some $p>1$, and prove the Hölder continuity of the solution.


  • Mohamad CharabatiInstitut de Mathématiques de Toulouse
    Université Paul Sabatier
    118 Route de Narbonne
    31062 Toulouse Cedex 09, France

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