## Differential and Integral Equations

- Differential Integral Equations
- Volume 12, Number 2 (1999), 275-293.

### Optimality principles and representation formulas for viscosity solutions of Hamilton-Jacobi equations. II. Equations of control problems with state constraints

#### Abstract

We prove local optimality principles for viscosity super and subsolutions of Hamilton-Jacobi equations with unbounded ingredients. We apply these results to characterize the (possibly multiple) discontinuous solutions of mixed Dirichlet and constrained boundary value problems.

#### Article information

**Source**

Differential Integral Equations, Volume 12, Number 2 (1999), 275-293.

**Dates**

First available in Project Euclid: 29 April 2013

**Permanent link to this document**

https://projecteuclid.org/euclid.die/1367265632

**Mathematical Reviews number (MathSciNet)**

MR1672758

**Zentralblatt MATH identifier**

1007.49016

**Subjects**

Primary: 49L25: Viscosity solutions

Secondary: 35D99: None of the above, but in this section 35F20: Nonlinear first-order equations

#### Citation

Soravia, Pierpaolo. Optimality principles and representation formulas for viscosity solutions of Hamilton-Jacobi equations. II. Equations of control problems with state constraints. Differential Integral Equations 12 (1999), no. 2, 275--293. https://projecteuclid.org/euclid.die/1367265632