Hopf-Lax formula for variational problems with non-constantdiscount

Juan Pablo Rincón-Zapatero

doi:10.3934/jgm.2009.1.357

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2009, Volume 1, Issue 3: 357-367. Doi: 10.3934/jgm.2009.1.357

This issue Previous Article The Hamilton-Jacobi theory and the analogy between classical and quantum mechanics Next Article On the geometry of the Hamilton-Jacobi-Bellman equation

Hopf-Lax formula for variational problems with non-constant discount

Juan Pablo Rincón-Zapatero^1,

1.
Departamento de Economía, Unversidad Carlos III de Madrid, 28903 Getafe (Madrid)

Received: February 28, 2009

Revised: May 31, 2009

Published: August 2009

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Abstract

We provide a Hop-Lax formula for variational problems with non-constant discount and deduce a dynamic programming equation. We also study some regularity properties of the value function.

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Mathematics Subject Classification: Primary: 35F25; Secondary: 49L20, 91B62.

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