Skip to main content
Log in

Autonomous Integral Functionals with Discontinuous Nonconvex Integrands: Lipschitz Regularity of Minimizers, DuBois—Reymond Necessary Conditions, and Hamilton—Jacobi Equations

  • Published:
Applied Mathematics & Optimization Submit manuscript

Abstract.

This paper is devoted to the autonomous Lagrange problem of the calculus of variations with a discontinuous Lagrangian. We prove that every minimizer is Lipschitz continuous if the Lagrangian is coercive and locally bounded. The main difference with respect to the previous works in the literature is that we do not assume that the Lagrangian is convex in the velocity. We also show that, under some additional assumptions, the DuBois—Reymond necessary condition still holds in the discontinuous case. Finally, we apply these results to deduce that the value function of the Bolza problem is locally Lipschitz and satisfies (in a generalized sense) a Hamilton—Jacobi equation.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Maso, ., Frankowska, . Autonomous Integral Functionals with Discontinuous Nonconvex Integrands: Lipschitz Regularity of Minimizers, DuBois—Reymond Necessary Conditions, and Hamilton—Jacobi Equations . Appl Math Optim 48, 39–66 (2003). https://doi.org/10.1007/s00245-003-0768-4

Download citation

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00245-003-0768-4

Navigation