## Differential and Integral Equations

- Differential Integral Equations
- Volume 12, Number 6 (1999), 849-886.

### A Hamilton-Jacobi equation with measures arising in $\Gamma$-convergence of optimal control problems

#### Abstract

We consider a Hamilton-Jacobi equation with a measure in the Hamiltonian arising from the $\Gamma$-limit of some optimal control problems. We give a definition of viscosity solution in this case, by adapting the method of the reparametrization of Dal Maso and Rampazzo [9].

#### Article information

**Source**

Differential Integral Equations, Volume 12, Number 6 (1999), 849-886.

**Dates**

First available in Project Euclid: 29 April 2013

**Permanent link to this document**

https://projecteuclid.org/euclid.die/1367241479

**Mathematical Reviews number (MathSciNet)**

MR1728034

**Zentralblatt MATH identifier**

1007.49015

**Subjects**

Primary: 49L25: Viscosity solutions

Secondary: 35B27: Homogenization; equations in media with periodic structure [See also 74Qxx, 76M50] 35B37 35F25: Initial value problems for nonlinear first-order equations 49L20: Dynamic programming method

#### Citation

Briani, Ariela. A Hamilton-Jacobi equation with measures arising in $\Gamma$-convergence of optimal control problems. Differential Integral Equations 12 (1999), no. 6, 849--886. https://projecteuclid.org/euclid.die/1367241479