Viscosity solutions of the Monge-Ampère equation with the right hand side in \(L^p\)
type: Item
instance of: scholarly article
title: Viscosity solutions of the Monge-Ampère equation with the right hand side in \(L^p\)
zbMATH Open document ID: 1223.35167
DOI: 10.4171/RLM/491
author: Anna Lisa Amadori
author: Barbara Brandolini
author: Cristina Trombetti
published in: Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni
publication date: 2008-06-25T00:00:00Z
review text: Summary: We compare various notions of solutions of Monge-Ampère equations with discontinuous functions in the right hand side. Precisely, we show that the weak solutions defined by \textit{N. S. Trudinger} [Commun. Partial Differ. Equations 22, No. 7--8, 1251--1261 (1997; Zbl 0883.35035)] can be obtained by the vanishing viscosity approximation method. Moreover, we investigate existence and uniqueness of \(L^p\)-viscosity solutions.
Mathematics Subject Classification ID: 35J65
Mathematics Subject Classification ID: 49L25
zbMATH DE Number: 5292678
zbMATH Keywords: viscosity solutions
zbMATH Keywords: weak solutions
zbMATH Keywords: Monge-Ampère equations
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.4171/rlm/491
OpenAlex ID: W1995109613
description: scientific article; zbMATH DE number 5292678