Journal of Convex Analysis, Vol. 07, No. 2, pp. 299-318 (2000)

Wellposedness in the Calculus of Variations

Bertirotti, Silvia

DIMA UniversitÓ di Genova 16146 Genova Italy

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.

Classification (MSC2000): 49K40

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