Geodesic
Wellposedness in the Calculus of Variations
Journal of convex analysis, Tome 7 (2000) no. 2, pp. 299-318

Voir la notice de l'article provenant de la source Heldermann Verlag

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 
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     author = {S. Bertirotti},
     title = {Wellposedness in the {Calculus} of {Variations}},
     journal = {Journal of convex analysis},
     pages = {299--318},
     publisher = {mathdoc},
     volume = {7},
     number = {2},
     year = {2000},
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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/