Well-posedness of nonconvex integral functionals

We find a sufficient condition which does not involve global convexity, guaranteeing well-posedness in a strong sense of the minimization of a multiple integral on the Sobolev space W1,1(Ω ℝm) with boundary datum equal to zero. In particular we apply our result to some nonconvex problems recently studied: functionals depending only on the gradient and radially symmetric functionals. © 2005 Society for Industrial and Applied Mathematics.