## Differential and Integral Equations

- Differential Integral Equations
- Volume 18, Number 6 (2005), 601-610.

### On the regularity of the solution of the Dirichlet problem for Hamilton-Jacobi equations

#### Abstract

We consider the Dirichlet problem for a class of Hamilton-Jacobi equations and we show that if the viscosity solution is semiconcave near the boundary then it is globally semiconcave. As an application, we discuss the particular case of eikonal-type equations. Finally, we describe a sort of stability property for the singular set of the semiconcave viscosity solution of Hamilton-Jacobi equations.

#### Article information

**Source**

Differential Integral Equations, Volume 18, Number 6 (2005), 601-610.

**Dates**

First available in Project Euclid: 21 December 2012

**Permanent link to this document**

https://projecteuclid.org/euclid.die/1356060172

**Mathematical Reviews number (MathSciNet)**

MR2136701

**Zentralblatt MATH identifier**

1212.35443

**Subjects**

Primary: 35F30: Boundary value problems for nonlinear first-order equations

Secondary: 49L25: Viscosity solutions

#### Citation

Albano, Paolo. On the regularity of the solution of the Dirichlet problem for Hamilton-Jacobi equations. Differential Integral Equations 18 (2005), no. 6, 601--610. https://projecteuclid.org/euclid.die/1356060172