Value Functions for Bolza Problems with Discontinuous Lagrangians and Hamilton-Jacobi Inequalities

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dc.creatorMaso, G. Dal
dc.creatorFrankowska, H.
dc.date2000-06-02
dc.date.accessioned2026-07-07T04:35:40Z
dc.date.available2026-07-07T04:35:40Z
dc.descriptionWe investigate the value function of the Bolza problem of the Calculus of Variations $$ V (t,x)=\inf \{\int_{0}^{t} L (y(s),y'(s))ds + ϕ(y(t)) : y \in W^{1,1} (0,t; R^n) ; y(0)=x \}, $$ with a lower semicontinuous Lagrangian $L$ and a final cost $ϕ$, and show that it is locally Lipschitz for $t>0$ whenever $L$ is locally bounded. It also satisfies Hamilton-Jacobi inequalities in a generalized sense. When the Lagrangian is continuous, then the value function is the unique lower semicontinuous solution to the corresponding Hamilton-Jacobi equation, while for discontinuous Lagrangian we characterize the value function by using the so called contingent inequalities.
dc.description33 pages. Control, Optimization and Calculus of Variations, to appear
dc.identifierhttps://arxiv.org/abs/math/0006013
dc.identifierhttp://arxiv.org/abs/math/0006013
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/59333
dc.subjectAnalysis of PDEs
dc.subject49L20; 49L25
dc.titleValue Functions for Bolza Problems with Discontinuous Lagrangians and Hamilton-Jacobi Inequalities
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