Geodesic
Wellposedness in the Calculus of Variations
Journal of convex analysis, Tome 7 (2000) no. 2, pp. 299-318 Cet article a éte moissonné depuis la source Heldermann Verlag

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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 : 49K40
Mots-clés : Calculus of variations, non convex integrals, wellposedness, variational convergence 
@article{JCA_2000_7_2_JCA_2000_7_2_a3,
     author = {S. Bertirotti},
     title = {Wellposedness in the {Calculus} of {Variations}},
     journal = {Journal of convex analysis},
     pages = {299--318},
     year = {2000},
     volume = {7},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JCA_2000_7_2_JCA_2000_7_2_a3/}
}
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S. Bertirotti. Wellposedness in the Calculus of Variations. Journal of convex analysis, Tome 7 (2000) no. 2, pp. 299-318. http://geodesic.mathdoc.fr/item/JCA_2000_7_2_JCA_2000_7_2_a3/