$C^{2,\alpha }$-estimate for Monge-Ampere equations with Hölder-continuous right hand side

Abstract

We present a somewhat new proof to the $C^{2,\alpha }$-aprori estimate for the uniform elliptic Monge-Ampere equations, in both the real and complex settings. Our estimates do not need to differentiate the equation, and only depends on the $C^{{\alpha }^{\prime }}-$norm of the right hand side of the equation, $0<\alpha <{\alpha }^{\prime }$.

arXiv comment14 pages, comments are welcome

References in corpus (12)

• Kahler-Einstein metrics on Fano manifolds, III: limits as cone angle approaches 2π and completion of the main proof
• Ricci flow on surfaces with conic singularities
• Kahler-Einstein metrics on Fano manifolds, II: limits with cone angle less than 2 π
• Kahler-Einstein metrics on Fano manifolds, I: approximation of metrics with cone singularities
• Conical Kahler-Einstein metric revisited
• The conical Kähler-Ricci flow on Fano manifolds
• Smooth approximations of the Conical Kahler-Ricci flows
• Bessel Functions, Heat Kernel and the Conical Kähler-Ricci Flow
• Geodesics in the space of Kähler cone metrics
• On the long time behaviour of the Conical Kähler- Ricci flows
• Existence of Weak Conical Kähler-Einstein Metrics Along Smooth Hypersurfaces
• A Remark On C^{2,α}-Regularity of the Complex Monge-Ampère Equation

Cited by in corpus (1)

• Local solution to the $G_2-$monopole equation with prescribed tangent cone and $G_2-$structure