Differential and Integral Equations

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

Paolo Albano

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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


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