MATHEMATICA BOHEMICA, Vol. 120, No. 4, pp. 411-430, 1995

Relaxation of vectorial variational problems

Tomas Roubicek

Tomas Roubicek, Mathematical Institute of the Charles University, Sokolovska 83, CZ-186 00 Praha 8, Czech Republic, and Institute of Information Theory and Automation, Academy of Sciences of the Czech Republic, Pod vodarenskou vezi 4, CZ-182 08 Praha 8, Czech Republic, e-mail:

Abstract: Multidimensional vectorial non-quasiconvex variational problems are relaxed by means of a generalized-Young-functional technique. Selective first-order optimality conditions, having the form of an Euler-Weiestrass condition involving minors, are formulated in a special, rather a model case when the potential has a polyconvex quasiconvexification.

Keywords: relaxed variational problems, Young measures, minors of gradients, optimality conditions, Weierstrass-type maximum principle

Classification (MSC91): 49K99, 49J99, 73V25, 35D05

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