A localization property of viscosity solutions to the Monge-Ampère equation and their strict convexity
type: Item
instance of: scholarly article
title: A localization property of viscosity solutions to the Monge-Ampère equation and their strict convexity
zbMATH Open document ID: 0704.35045
DOI: 10.2307/1971509
author: Luis Caffarelli
published in: Annals of Mathematics. Second Series
publication date: 1990-01-01T00:00:00Z
review text: The author considers viscosity solutions of the Monge-Ampère equation \[ (1)\quad 0<\lambda_ 1\leq \det D^ 2u\leq \lambda_ 2 \] with \(C^{1,\alpha}\) boundary data \((\alpha >1-2/n)\). Assume that \(u\geq 0\) satisfies (1) and that the convex set \(\{u=0\}\) is not a point. Then this set cannot have extremal points in the interior of the domain of definition of u.
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 35B50
zbMATH DE Number: 4154995
zbMATH Keywords: viscosity solutions
zbMATH Keywords: Monge-Ampère equation
zbMATH Keywords: convex
zbMATH Keywords: extremal points
reviewed by: G. Dziuk
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2307/1971509
OpenAlex ID: W2330976889
description: scientific article; zbMATH DE number 4154995