This paper proves new results of existence of minimizers for the nonconvex integralOur 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.
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