Abstract

We consider the stability of solutions of variational problems with respect to perturbations of the integrand, raised by S. M. Ulam [A Collection of Mathematical Problems, Interscience, Los Alamos, 1958]. We prove some results concerning Ulam's problem by using the theory of wellposedness. We consider the notion of wellposedness introduced by T. Zolezzi [Well-posedness criteria in optimization with application to the calculus of variations, Nonlinear Anal. TMA 25 (1995) 437-453] and we deal with perturbations of the integrands related to variational convergence. Moreover some criteria to obtain variational convergence of sequences of non-convex integrals are given.

Author information

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Silvia Bertirotti

DIMA, Università di Genova, 16146 Genova, Italy

Keywords

  • Calculus of variations
  • non convex integrals
  • wellposedness
  • variational convergence

Mathematics Subject Classification

49K40

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Suggested citation

S. Bertirotti. “Wellposedness in the Calculus of Variations.” Journal of Convex Analysis 7 (2000), No. 2, 299–318. https://doi.org/10.68381/jca07015

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Published by Heldermann Verlag, 2000. Rights now held by Banach Press LLC.