Existence and regularity for scalar minimizers of affine nonconvex simple integrals Original Research Article

Existence of AC minimizers View the MathML source is proved for the nonconvex integral View the MathML source, under the general hypotheses of lower semicontinuity, boundedness below, and superlinear growth at infinity in x′(·). Any nonconvex function View the MathML source will do, provided it is convex at ξ=0. Moreover, minimizers are shown to satisfy several regularity properties, under adequate hypotheses.