Pubblicazioni

Autori:

Marigonda, Antonio; Siconolfi, Antonio

Titolo:

Metric formulae for nonconvex Hamilton-Jacobi equations and applications

Anno:

2011

Tipologia prodotto:

Articolo in Rivista

Tipologia ANVUR:

Articolo su rivista

Lingua:

Inglese

Formato:

A Stampa

Referee:

Sì

Nome rivista:

Advances in Differential Equations

ISSN Rivista:

1079-9389

N° Volume:

7-8

Intervallo pagine:

691-724

Parole chiave:

Nonconvex Hamilton-Jacobi equations; viscosity solutions; Aubry-Mather theory

Breve descrizione dei contenuti:

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 $\varepsilon >0$.

Id prodotto:

60500

Handle IRIS:

11562/344804

depositato il:

15 maggio 2011

ultima modifica:

29 novembre 2022

Citazione bibliografica:

Marigonda, Antonio; Siconolfi, Antonio, Metric formulae for nonconvex Hamilton-Jacobi equations and applications «Advances in Differential Equations» , vol. 7-8 , 2011 , pp. 691-724

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