Nonconcentrating generalized Young functionals

Abstract. The Young measures, used widely for relaxation of various optimization prob-lems, can be naturally understood as certain functionals on suitable space of integrands,which allows readily various generalizations. The paper is focused on such functionalswhich can be attained by sequences whose “energy” (=pth power) does not concentratein the sense that it is relatively weakly compact in L 1 (Ω). Straightforward applicationsto coercive optimization problems are briefly outlined.Keywords: Young measures, generalizations, relative L 1 -weak compactness, coercive op-timization problems, nonconcentration of energyClassification: 49N60 1. IntroductionMore than half a century ago, L.C. Young [19] introduced a tool, called nowYoung measures, to hold a certain “limit information” about oscillations that mayappear in nonconvex variational problems. This was later widely exploited alsoin optimal control and game theory, where oscillation effects typically arise, aswell. Let us recall that a Young measure ν on a domain Ω ⊂ R