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

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

ALBANO, PAOLO
2005

Abstract

We consider the Dirichlet problem for a class of Hamilton- Jacobi equations and we show that if the viscosity solution is semicon- cave near the boundary then it is globally semiconcave. As an applica- tion, we discuss the particular case of eikonal-type equations. Finally, we describe a sort of stability property for the singular set of the semi- concave viscosity solution of Hamilton-Jacobi equations.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/7513
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