Nonexistence of solutions in nonconvex multidimensional variational problems

In the scaler n-dimensional situation, the extreme points in the set of cer tain gradient L-P-Young measures are studied. For n = 1, such Young measure s must he composed from Diracs, while for n greater than or equal to 2 ther e are non-Dirac extreme points among them. for n greater than or equal to 3 . some are even weakly* continuous. This is used to construct nontrivial ex amples of nonexistence of solutions of the minimization-type variational pr oblem integral (Omega) W(x, delu) dx with a Caratheodory (if n greater than or equal to 2) or even continuous (if n greater than or equal to 3) integr and W.