Geodesic
Nonexistence of Solutions in Nonconvex Multidimensional Variational Problems
Journal of convex analysis, Tome 7 (2000) no. 2, pp. 427-435

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

In the scalar n-dimensional situation, the extreme points in the set of certain gradient Lp-Young measures are studied. For n = 1, such Young measures must be composed from Diracs, while for n ≥ 2 there are non-Dirac extreme points among them, for n ≥ 3, some are even weakly* continuous. This is used to construct nontrivial examples of nonexistence of solutions of the minimization-type variational problem Integral0 W(x, nabla u) dx with a Caratheodory (if n ≥ 2) or even continuous (if n ≥ 3) integrand W.
Classification : 49J99
Mots-clés : Gradient Young measures, extreme points, Cantor sets, integration factors, Bauer principle, nonattainment 
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     author = {T. Roub{\'\i}cek and V. Sverak},
     title = {Nonexistence of {Solutions} in {Nonconvex} {Multidimensional} {Variational} {Problems}},
     journal = {Journal of convex analysis},
     pages = {427--435},
     publisher = {mathdoc},
     volume = {7},
     number = {2},
     year = {2000},
     url = {http://geodesic.mathdoc.fr/item/JCA_2000_7_2_JCA_2000_7_2_a10/}
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T. Roubícek; V. Sverak. Nonexistence of Solutions in Nonconvex Multidimensional Variational Problems. Journal of convex analysis, Tome 7 (2000) no. 2, pp. 427-435. http://geodesic.mathdoc.fr/item/JCA_2000_7_2_JCA_2000_7_2_a10/