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Journal Article

Nonexistence of solutions in nonconvex multidimensional variational problems

Roubíček Tomáš, Šverák V.

: Journal of Convex Analysis vol.7, 99 (2000), p. 427-436

: AV0Z1075907

(eng): 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>1 there are non-Dirac extreme points among them, for n>2, some are even weakly* continuous. This is used to construct nontrivial examples of nonexistence of solutions of the minimization-type variational problems.

: 12A

: BA

2019-01-07 08:39