Schauder estimates for degenerate Monge-Ampere equations and smoothness of the eigenfunctions

• 成果类型: Article
• 署名作者: Le, Nam Q.; Savin, Ovidiu
• 署名单位: Indiana University System; Indiana University Bloomington; Columbia University
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-016-0677-1
• 发表日期: 2017
• 页码: 389-423
• 关键词: boundary-regularity; dirichlet problem

摘要

We obtain estimates up to the boundary for solutions to degenerate Monge-AmpSre equations of the type det D(2)u = f in Omega, f similar to dist(alpha)(., partial derivative Omega) near partial derivative Omega, alpha > 0. As a consequence we obtain global estimates up to the boundary for the eigenfunctions of the Monge-AmpSre operator on smooth, bounded, uniformly convex domains in R-n.