Existence of vector minimizers for nonconvex 1-dim integrals with almost convex Lagrangian

This paper proves new results of existence of minimizers for the nonconvex integral , among the AC functions with x(a)=A, x(b)=B. Our Lagrangian L(⋅) is e.g. lsc with superlinear growth, assuming +∞ values freely. We replace convexity by almost convexity, a hypothesis which in the radial superlinear case L(s,ξ)=f(s,|ξ|) is automatically satisfied provided f(s,⋅) is convex at zero.