A localization theorem and boundary regularity for a class of degenerate Monge Ampere equations

By Ovidiu Savin. 2013

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We consider degenerate Monge-Ampere equations of the type $$\det D^2 u= f \quad \{in $\Om$}, \quad \quad f \sim \, d_{\p \Om}^\alpha \quad \{near $\p \Om$,}$$ where $d_{\p \Om}$ represents the distance to the boundary of the domain $\Om$ and $\alpha>0$ is a positive power. We obtain $C^2$ estimates at the boundary under natural conditions on the boundary data and the right hand side. Similar estimates in two dimensions were obtained by J.X. Hong, G. Huang and W. Wang.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/b5175b176d4376f619bd6f902ffa95bb15d19dbf

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In Applied Mathematics

In Geometry and Topology

Citations in the corpus

On the Monge-Amp\`ere equation (2018, methodology): “Once this is achieved, Le and Savin conclude the global smoothness of ψ1 by applying Schauder estimates for Grushin-type operators: Corollary 6.4.”