We consider an Hamilton-Jacobi equation of the form H( x, Du) = 0 x is an element of Omega R-N, ( 1) where H( x, p) is assumed Borel measurable and quasi-convex in p. The notion of Monge solution, introduced by Newcomb and Su, is adapted to this setting making use of suitable metric devices. We establish the comparison principle for Monge sub and supersolution, existence and uniqueness for equation ( 1) coupled with Dirichlet boundary conditions, and a stability result. The relation among Monge and Lipschitz subsolutions is also discussed.

Monge solutions for discontinuous Hamiltonians / Ariela, Briani; Davini, Andrea. - In: ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS. - ISSN 1262-3377. - STAMPA. - 11:11(2005), pp. 229-251. [10.1051/cocv:2005004]

Monge solutions for discontinuous Hamiltonians

DAVINI, ANDREA
2005

Abstract

We consider an Hamilton-Jacobi equation of the form H( x, Du) = 0 x is an element of Omega R-N, ( 1) where H( x, p) is assumed Borel measurable and quasi-convex in p. The notion of Monge solution, introduced by Newcomb and Su, is adapted to this setting making use of suitable metric devices. We establish the comparison principle for Monge sub and supersolution, existence and uniqueness for equation ( 1) coupled with Dirichlet boundary conditions, and a stability result. The relation among Monge and Lipschitz subsolutions is also discussed.
2005
finsler metric; lax formula; viscosity solution
01 Pubblicazione su rivista::01a Articolo in rivista
Monge solutions for discontinuous Hamiltonians / Ariela, Briani; Davini, Andrea. - In: ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS. - ISSN 1262-3377. - STAMPA. - 11:11(2005), pp. 229-251. [10.1051/cocv:2005004]
File allegati a questo prodotto
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/140189
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 19
  • ???jsp.display-item.citation.isi??? 22
social impact