Treffer: Uniqueness of solutions to Hamilton-Jacobi equations arising in the Calculus of Variations
Title:
Uniqueness of solutions to Hamilton-Jacobi equations arising in the Calculus of Variations
Authors:
Source:
Optimal control and partial differential equations (Paris, 4 December 2000). :335-345
Publisher Information:
Amsterdam; Tokyo: IOS Press, Ohmsha, 2001.
Publication Year:
2001
Physical Description:
print, 12 ref
Original Material:
INIST-CNRS
Subject Terms:
Control theory, operational research, Automatique, recherche opérationnelle, Computer science, Informatique, Mathematics, Mathématiques, Sciences exactes et technologie, Exact sciences and technology, Sciences et techniques communes, Sciences and techniques of general use, Mathematiques, Mathematics, Analyse numérique. Calcul scientifique, Numerical analysis. Scientific computation, Analyse numérique, Numerical analysis, Méthodes numériques en programmation mathématique, optimisation et calcul variationnel, Numerical methods in mathematical programming, optimization and calculus of variations, Optimisation et calcul variationnel numériques, Numerical methods in optimization and calculus of variations, Convexité, Convexity, Convexidad, Equation Hamilton Jacobi, Hamilton Jacobi equation, Ecuación Hamilton Jacobi, Solution viscosité, Viscosity solution, Solución viscosidad, Sous différentiel, Subdifferential, Subdiferencial, Unicité solution, Solution uniqueness, Unicidad solución, Viabilité, Viability, Viabilidad, Fonction semicontinue
Document Type:
Konferenz
Conference Paper
File Description:
text
Language:
English
Author Affiliations:
SISSA, via Berirat 2-4, 34014 Trieste, Italy
CNRS, ERS2064, Centre de Recherche Viabilité, Jeux, Contrôle, Université de Paris-Dauphine, 75775 Paris, France
CNRS, ERS2064, Centre de Recherche Viabilité, Jeux, Contrôle, Université de Paris-Dauphine, 75775 Paris, France
Rights:
Copyright 2001 INIST-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
Notes:
Mathematics
Accession Number:
edscal.1008024
Database:
PASCAL Archive
Weitere Informationen
We prove the uniqueness of the viscosity solution to the Hamilton-Jacobi equation associated with a Bolza problem of the Calculus of Variations, assuming that the Lagrangian is autonomous, continuous, superlinear, and satisfies the usual convexity hypothesis. Under the same assumptions we prove also the uniqueness, in a class of lower semicontinuous functions, of a slightly different notion of solution, where classical derivatives are replaced only by subdifferentials. These results follow from a new comparison theorem for lower semicontinuous viscosity supersolutions of the Hamilton-Jacobi equation, that is proved in the general case of lower semicontinuous Lagrangians.