Existence of solutions for non level-convex problems in the supremal form

It is well known that lower semicontinuity of functionals in
the supremal form F(u)=esssupx¸ƒ¶ f(Þu(x))is related to the
level-convexity of the supremand f . We adress the problem of
existence of solutions for the Dirichlet boundary problem in the lack
of this convexity condition relating it with some differential
inclusion problem. This is a joint work with E. Zappale.