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Journal of Convex Analysis 07 (2000), No. 2, 299--318
Copyright Heldermann Verlag 2000

Wellposedness in the Calculus of Variations

Silvia Bertirotti
DIMA, UniversitÓ di Genova, 16146 Genova, Italy

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.

Keywords: Calculus of variations, non convex integrals, wellposedness, variational convergence.

MSC: 49K40

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