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.
Albano P. (2005). On the regularity of the solution of the Dirichlet problem for Hamilton-Jacobi equations. DIFFERENTIAL AND INTEGRAL EQUATIONS, 18, 601-610.
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.File in questo prodotto:
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