An Overview on Existence of Vector Minimizers for Almost Convex 1—dim Integrals

Abstract

We present results of existence of minimizers for the nonconvex integralis, e.g., lsc with coercive growth, assuming +∞ values freely. We replace convexity by almost convexity, a hypothesis which in the radial case L (s, ξ) = f (s, |ξ|) is automatically satisfied provided f (s, • ) has superlinear growth and is convex at zero.