# Publications

## Metric formulae for nonconvex Hamilton-Jacobi equations and applications  (2011)

Authors:
Antonio Marigonda; Siconolfi Antonio
Title:
Metric formulae for nonconvex Hamilton-Jacobi equations and applications
Year:
2011
Type of item:
Articolo in Rivista
Tipologia ANVUR:
Articolo su rivista
Nations of authors:
ITALIA
Language:
Inglese
Format:
A Stampa
Referee:
Name of journal:
ISSN of journal:
1079-9389
N° Volume:
7-8
Page numbers:
691-724
Keyword:
Nonconvex Hamilton-Jacobi equations, viscosity solutions, Aubry-Mather theory
Short description of contents:
We consider the Hamilton-Jacobi equation $H(x,Du)=0$ in $\mathbb R^n$, with $H$ non enjoying any convexity properties in the second variable. Our aim is to establish existence and nonexistence theorems for viscosity solutions of associated Dirichlet problems, find representation formulae and prove comparison principles. Our analysis is based on the introduction of a metric intrinsically related to the $0$--sublevels of the Hamiltonian, given by an inf-sup game theoretic formula. We also study the case where the equation is critical, i.e. $H(x,Du)= - \varepsilon$ does not admit any viscosity subsolution, for $\varepsilon >0$.
Product ID:
60500
Handle IRIS:
11562/344804
Deposited On:
May 15, 2011
November 2, 2016
Bibliographic citation:
Antonio Marigonda; Siconolfi Antonio, Metric formulae for nonconvex Hamilton-Jacobi equations and applications «Advances in Differential Equations» , vol. 7-82011pp. 691-724

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Related projects
Title Department Managers
Fenomeni di propagazione di fronti e problemi di omogeneizzazione (GNAMPA 2010 ESTERNO) Department Informatica Antonio Marigonda