A note on comparison principles for viscosity solutions of fully nonlinear second order partial differential equations
type: Item
instance of: scholarly article
title: A note on comparison principles for viscosity solutions of fully nonlinear second order partial differential equations
zbMATH Open document ID: 0939.35013
author: Dirk Horstmann
published in: Hokkaido Mathematical Journal
publication date: 2000-06-19T00:00:00Z
review text: The goal of this paper is to compare viscosity sub- and supersolutions of fully nonlinear second order elliptic partial differential equations \(F(u,Du, D^2u)=0\) in \(\Omega\subset \mathbb{R}^N\), with Dirichlet boundary data \(u=f\) on \(\partial \Omega\), where \(F\in C(\mathbb{R}\times \mathbb{R}^N\times S(N))\) and \(f\in C(\partial \Omega)\). Two comparison principles are established.
Mathematics Subject Classification ID: 35B05
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 35J65
zbMATH DE Number: 1331849
zbMATH Keywords: viscosity solutions
zbMATH Keywords: comparison principles
zbMATH Keywords: \(\omega\)-ellipticity
reviewed by: Narcisa Apreutesei
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.14492/hokmj/1351001216
OpenAlex ID: W1997383967
DOI: 10.14492/HOKMJ/1351001216
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description: scientific article; zbMATH DE number 1331849