Viscosity solutions of monotone systems for Dirichlet problems
type: Item
instance of: scholarly article
title: Viscosity solutions of monotone systems for Dirichlet problems
zbMATH Open document ID: 0823.35025
author: S. Koike
author: Markos Katsoulakis
published in: Differential and Integral Equations
publication date: 1994-03-24T00:00:00Z
review text: Existence of viscosity solutions for fully nonlinear elliptic systems of second order of the form \(F_ k (x, u, D_ k u, D^ 2 u_ k) =0\) for \(x\in G\), \(k= 1,\dots, m\), where \(G\) is a smooth bounded domain in \(\mathbb{R}^ N\) is proved in the case, where the system is monotone in a suitable sense. This extends some previous work by different people, including the authors. Definitions of multivalued sub- and supersolutions are first given and then a uniqueness theorem is proved. A comparison result for monotone systems is also proved and this allows to compare nontangential semicontinuous sub- and supersolutions. Finally the existence result is proved.
Mathematics Subject Classification ID: 35D05
Mathematics Subject Classification ID: 35J45
Mathematics Subject Classification ID: 35J65
zbMATH DE Number: 527354
zbMATH Keywords: fully nonlinear elliptic systems
zbMATH Keywords: multivalued sub- and supersolutions
zbMATH Keywords: uniqueness
reviewed by: Jesús Hernández
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 527354