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We consider the problem of minimizing autonomous, simple integrals like (P) min T 0 f x(t) , x (t) dt : x ∈ AC([0 , T ]) with x(0) = x0 and x(T) = xT where f : R×R → [0 , ∞] is a possibly nonconvex function with either superlinear or slow growth at infinity. Assuming that the relaxed problem (P * *) obtained from (P) by replacing f with its convex envelope… (More)

We study the existence of solutions to Bolza problems involving a special class of one dimensional, nonconvex integrals. These integrals describe the possibly singular, radial deformations of certain rubber-like materials called Blatz-Ko materials.

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