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

2013/03/12 by Ovidiu Savin, Savin, Ovidiu
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.1303.2897

openalex publication_date 2013/03/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider degenerate Monge-Ampere equations of the type
det D² u= f\n
quad
in
Om,
quad
quad f
sim
, d
_p
Om^
alpha
quad
near
p\n
Om, where d _{p Om} represents the distance to the boundary of the\ndomain Om and \α>0 is a positive power. We obtain C² estimates at\nthe boundary under natural conditions on the boundary data and the right hand\nside. Similar estimates in two dimensions were obtained by J.X. Hong, G. Huang\nand W. Wang.\n

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