Uniqueness of solutions to Hamilton-Jacobi equations arising in the Calculus of Variations

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dc.creatorMaso, G. Dal
dc.creatorFrankowska, H.
dc.date2000-06-02
dc.date.accessioned2026-07-07T04:35:41Z
dc.date.available2026-07-07T04:35:41Z
dc.descriptionWe prove the uniqueness of the viscosity solution to the Hamilton-Jacobi equation associated with a Bolza problem of the Calculus of Variations, assuming that the Lagrangian is autonomous, continuous, superlinear, and satisfies the usual convexity hypothesis. Under the same assumptions we prove also the uniqueness, in a class of lower semicontinuous functions, of a slightly different notion of solution, where classical derivatives are replaced only by subdifferentials. These results follow from a new comparison theorem for lower semicontinuous viscosity supersolutions of the Hamilton-Jacobi equation, that is proved in the general case of lower semicontinuous Lagrangians.
dc.description14 pages
dc.identifierhttps://arxiv.org/abs/math/0006015
dc.identifierhttp://arxiv.org/abs/math/0006015
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/59335
dc.subjectAnalysis of PDEs
dc.subject49L20; 49L25
dc.titleUniqueness of solutions to Hamilton-Jacobi equations arising in the Calculus of Variations
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