A localization property at the boundary for the Monge-Ampere equation

2010/10/08 by Ovidiu Savin, Savin, Ovidiu · 1 citation
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1010.1745

openalex publication_date 2010/10/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider Monge-Ampere equations with bounded right hand side and we study the geometric properties of sections centered at a boundary point. We prove that under natural boundary conditions such sections are equivalent to ellipsoids.

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