Hölder regularity for solutions to complex Monge-Ampère equations

• Autorzy: Mohamad Charabati
• Języki publikacji: EN

Abstrakty

EN

We consider the Dirichlet problem for the complex Monge-Ampère equation in a bounded strongly hyperconvex Lipschitz domain in ℂⁿ. 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 $𝓒^{1,1}$ and the right hand side has a density in $L^{p}(Ω)$ for some p > 1, and prove the Hölder continuity of the solution.

Kategorie tematyczne

• 32U15: General pluripotential theory
• 32W20: Complex Monge-Amp\`ere operators
• 35J96: Elliptic Monge-Amp\`ere equations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2015
• Tom: 113
• Numer: 2
• Strony: 109-127

Daty

wydano

2015

Twórcy

autor

Mohamad Charabati

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

Identyfikatory

DOI

10.4064/ap113-2-1