Boundary regularity for Monge-Ampère equations with unbounded right hand side

DOI10.2422/2036-2145.201805_007zbMath1482.35104arXiv1803.10304OpenAlexW2963362201MaRDI QIDQ5003168

Ovidiu V. Savin, Qian Zhang

Publication date: 20 July 2021

Published in: ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE (Search for Journal in Brave)

Abstract: We consider Monge-Amp`ere equations with right hand side $f$ that degenerate to $infty$ near the boundary of a convex domain $Omega$, which are of the type $$mathrm{det};D^2 u=fquadmathrm{in};Omega,quadquad fsim d^{-alpha}_{partialOmega}quadmathrm{near};partialOmega,$$ where $d_{partialOmega}$ represents the distance to $partial Omega$ and $-alpha$ is a negative power with $alphain(0,2)$. We study the boundary regularity of the solutions and establish a localization theorem for boundary sections.

Full work available at URL: https://arxiv.org/abs/1803.10304

zbMATH Keywords

regularityMonge-Ampère equationlocalization theoremconvex solutionboundary section

Mathematics Subject Classification ID

Degenerate elliptic equations (35J70) Monge-Ampère equations (35J96)

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