Differential and Integral Equations

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

Paolo Albano

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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

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

First available in Project Euclid: 21 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35F30: Boundary value problems for nonlinear first-order equations
Secondary: 49L25: Viscosity solutions


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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