Relaxation of vectorial variational problems

Tomáš Roubíček

Displaying similar documents to “Relaxation of vectorial variational problems”

Optimality conditions for nonconvex variational problems relaxed in terms of Young measures

Tomáš Roubíček (1998)

Kybernetika

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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.

Examples from the calculus of variations. II. A degenerate problem

Jan Chrastina (2000)

Mathematica Bohemica

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Continuing the previous Part I, the degenerate first order variational integrals depending on two functions of one independent variable are investigated.

On results of Jan Mařík in the theory of derivatives

Luděk Zajíček (1996)

Mathematica Bohemica

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Results of Jan Marik on the theory of derivatives of real functions are described.

On condensing discrete dynamical systems

Valter Šeda (2000)

Mathematica Bohemica

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In the paper the fundamental properties of discrete dynamical systems generated by an $α$ -condensing mapping ( $α$ is the Kuratowski measure of noncompactness) are studied. The results extend and deepen those obtained by M. A. Krasnosel’skij and A. V. Lusnikov in []. They are also applied to study a mathematical model for spreading of an infectious disease investigated by P. Takac in [], [].