On viscosity solutions of the Hamilton-Jacobi equation
type: Item
instance of: scholarly article
title: On viscosity solutions of the Hamilton-Jacobi equation
zbMATH Open document ID: 0968.49021
author: Thomas Strömberg
published in: Hokkaido Mathematical Journal
publication date: 2001-08-28T00:00:00Z
review text: The author investigates the value function \(V(t,x)\) of a Bolza problem, namely to minimize \[ \varphi(X(0)) + \int_0^t L(X(\tau),\dot{X}(\tau)) d\tau ,\quad X(t) = x . \] He proves that, under certain assumptions on the Lagrangian and on \(\varphi\), the value function is a viscosity subsolution of the associated Hamilton-Jacobi equation, and that it is locally Lipschitz continuous. He also proves some uniqueness and comparison results.
Mathematics Subject Classification ID: 49L25
zbMATH DE Number: 1396094
zbMATH Keywords: viscosity solution
zbMATH Keywords: Hamilton-Jacobi equation
zbMATH Keywords: comparison
zbMATH Keywords: uniqueness
zbMATH Keywords: Bolza problem
reviewed by: Martin Brokate
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.14492/hokmj/1351001232
OpenAlex ID: W1996116636
DOI: 10.14492/HOKMJ/1351001232
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description: scientific article; zbMATH DE number 1396094