Hölder regularity for solutions to complex Monge–Ampère equations

Mohamad Charabati¹

¹ Institut de Mathématiques de Toulouse Université Paul Sabatier 118 Route de Narbonne 31062 Toulouse Cedex 09, France

Annales Polonici Mathematici, Tome 113 (2015) no. 2, pp. 109-127.

Résumé

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.

Détail

DOI : 10.4064/ap113-2-1

Mots-clés : consider dirichlet problem complex monge amp equation bounded strongly hyperconvex lipschitz domain nbsp mathbb first sharp estimate modulus continuity solution boundary continuous right side has continuous density consider boundary value function mathcal right side has density varomega prove lder continuity solution