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

Tomáš Roubíček

Kybernetika (1998)

  • Volume: 34, Issue: 3, page [335]-347
  • ISSN: 0023-5954

Abstract

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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.

How to cite

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Roubíček, Tomáš. "Optimality conditions for nonconvex variational problems relaxed in terms of Young measures." Kybernetika 34.3 (1998): [335]-347. <http://eudml.org/doc/33358>.

@article{Roubíček1998,
abstract = {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.},
author = {Roubíček, Tomáš},
journal = {Kybernetika},
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},
language = {eng},
number = {3},
pages = {[335]-347},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Optimality conditions for nonconvex variational problems relaxed in terms of Young measures},
url = {http://eudml.org/doc/33358},
volume = {34},
year = {1998},
}

TY - JOUR
AU - Roubíček, Tomáš
TI - Optimality conditions for nonconvex variational problems relaxed in terms of Young measures
JO - Kybernetika
PY - 1998
PB - Institute of Information Theory and Automation AS CR
VL - 34
IS - 3
SP - [335]
EP - 347
AB - 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.
LA - eng
KW - 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
UR - http://eudml.org/doc/33358
ER -

References

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