Characterization of homogeneous scalar variational problems solvable for all boundary data

Abstract: "In this paper we introduce a condition on lower semicontinuous integrands L : R[superscript n] -> R both necessary and sufficient for all problems of the form J(u) = [integral subscript omega] L(Du)dx -> min, u [element of] W[superscript 1,1]([omega]), u/[subscript delta omega] = f to have a solution, provided [omega] and f are sufficiently regular or certain conditions on growth of L at infinity are assumed."