Well-posedness of Nonconvex Integral Functionals

We find a sufficient condition guaranteeing well-posedness in a strong sense of the minimization of a multiple integral on the Sobolev space W^1,1(Ω; R^m) with boundary datum equal to zero. We remark that this condition does not involve global convexity of the integrand and therefore it allows us to find well-posedness properties of two classes of nonconvex problems recently studied: functionals depending only on the gradient and radially symmetric functionals.