Limit of the infinite horizon discounted Hamilton-Jacobi equation

Renato Iturriaga; Héctor Sánchez-Morgado

doi:10.3934/dcdsb.2011.15.623

Article Contents

2011, Volume 15, Issue 3: 623-635. Doi: 10.3934/dcdsb.2011.15.623

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Limit of the infinite horizon discounted Hamilton-Jacobi equation

Renato Iturriaga^1, and
Héctor Sánchez-Morgado^2,

1.
CIMAT, A.P. 402, 3600, Guanajuato. Gto
2.
I. de Matemáticas, UNAM, Cd. Universitaria, México, D.F. 04510

Received: October 2007

Revised: March 2010

Published: October 2011

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Abstract

Motivated by the infinite horizon discounted problem, we study the convergence of solutions of the Hamilton Jacobi equation when the discount vanishes. If the Aubry set consists in a finite number of hyperbolic critical points, we give an explicit expression for the limit. Additionaly, we give a new characterization of Mañé's critical value as for wich the set of viscosity solutions is equibounded.

Keywords:

Hamilton-Jacobi equation.

Mathematics Subject Classification: Primary: 37J50, 49L25; Secondary: 70H20.

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References

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