Hamilton-Jacobi equations in infinite dimensions. I: Uniqueness of viscosity solutions
type: Item
instance of: scholarly article
title: Hamilton-Jacobi equations in infinite dimensions. I: Uniqueness of viscosity solutions
zbMATH Open document ID: 0627.49013
DOI: 10.1016/0022-1236(85)90011-4
author: Michael G. Crandall
author: P.-L. Lions
published in: Journal of Functional Analysis
publication date: 1985-01-01T00:00:00Z
review text: In a series of previous papers the authors have introduced the concept of viscosity solutions for Hamilton-Jacobi equations in \({\mathbb{R}}^ n\) of the form \(H(x,u,Du)=0\) and proved existence and uniqueness for a large class of Hamiltonian functions H. This is a first work of a series of papers where the authors extend their beautiful theory to infinite dimensional Banach spaces with the Radon-Nikodym property. The main result of this paper is a uniqueness theorem of viscosity solutions under appropriate conditions on H which resemble those from the finite dimensional case. A key ingredient of the uniqueness in the infinite dimensional setting is Stegall's variational principle.
Mathematics Subject Classification ID: 49L99
Mathematics Subject Classification ID: 35D05
Mathematics Subject Classification ID: 35F20
Mathematics Subject Classification ID: 46B99
zbMATH DE Number: 4019853
zbMATH Keywords: viscosity solutions
zbMATH Keywords: Hamilton-Jacobi equations
zbMATH Keywords: infinite dimensional Banach spaces with the Radon-Nikodym property
MaRDI profile type: Publication
full work available at URL: 0022-1236(85)90011-4
OpenAlex ID: W1979308690
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description: scientific article; zbMATH DE number 4019853