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Existence of Lipschitzian solutions to the classical problem of the calculus of variations in the autonomous case

✍ Scribed by A. Cellina; A. Ferriero

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
83 KB
Volume
20
Category
Article
ISSN
0294-1449

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✦ Synopsis

Under general growth assumptions, that include some cases of linear growth, we prove existence of Lipschitzian solutions to the problem of minimizing b a L(x(s), x (s)) ds with the boundary conditions x(a) = A, x(b) = B.  2003 Éditions scientifiques et médicales Elsevier SAS MSC: 49N60; 49J65 Keywords: Calculus of variations; Existence and Lipschitzianity of solutions RÉSUMÉ. -Dans l'article on démontre l'existence de solutions Lipschitziennes du problème de minimiser b a L(x(s), x (s)) ds, x(a) = A, x(b) = B, avec des conditions faibles, de croissance, qui comprennent des cas de croissance linéaire.

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