On the local semiconcavity of the solutions of the eikonal equation |
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Authors: | Paolo Albano |
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Affiliation: | Dipartimento di Matematica, Università di Bologna, Piazza di Porta San Donato 5, I-40127 Bologna, Italy |
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Abstract: | We show that if the Hamiltonian is locally semiconvex with respect to the state variables and strictly convex with respect to the gradient then every viscosity solution of the eikonal equation is locally semiconcave. Furthermore, in the 1D case, we show that every viscosity solution of the eikonal equation is semiconcave if and only if the Hamiltonian is Lipschitz continuous with respect to the state variable. |
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Keywords: | Viscosity solutions Eikonal equation Semiconcavity |
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