Nonexistence of solutions in nonconvex multidimensional variational problems

In the scalar n-dimensional situation, the extreme points in the set of certain gradient L-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

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