Regularity of solutions to the Dirichlet problem for Monge-Amp `ere\n equations

2015/11/05 by Mohamad Charabati, Charabati, Mohamad · 2 citations
Mathematics · #32U15 #32W20 #Complex Variables (math.CV) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1511.01858

openalex publication_date 2015/11/05 · openalex created_date 2022/10/06 · openalex updated_date 2026/07/28

Abstract

We study H "older continuity of solutions to the Dirichlet problem for\nmeasures having density in L^p, p>1, with respect to Hausdorff-Riesz\nmeasures of order 2n-2+\ε for 0<\ε \≤ 2, in a bounded\nstrongly hyperconvex Lipschitz domain and the boundary data belongs to \nC^0,\α(\∂ \Ω), 0<\α \≤ 1.\n

Cited by

• Hölder Regularity of Dirichlet Problem For The Complex Monge-Ampère Equation
• α-Hölder Integrability Exponent

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