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Keywords:
nonconvex variational problem; Sobolev space; Young measure; convex compactification theory; Euler-Lagrange equation; Weierstrass condition; minimum-energy type; optimality conditions
nonconvex variational problem; Sobolev space; Young measure; convex compactification theory; Euler-Lagrange equation; Weierstrass condition; minimum-energy type; optimality conditions
Summary:
The scalar nonconvex variational problems of the minimum-energy type on Sobolev spaces are studied. As the Euler–Lagrange equation dramatically looses selectivity when extended in terms of the Young measures, the correct optimality conditions are sought by means of the convex compactification theory. It turns out that these conditions basically combine one part from the Euler–Lagrange equation with one part from the Weierstrass condition.
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