Email this article Generalized Weierstrass Condition in the Classical Calculus of Variations
- Authors: Arutyunov A.V.1,2,3
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Affiliations:
- Lomonosov Moscow State University
- Peoples’ Friendship University of Russia
- Derzhavin Tambov State University
- Issue: Vol 55, No 1 (2019)
- Pages: 75-83
- Section: Control Theory
- URL: https://journal-vniispk.ru/0012-2661/article/view/154922
- DOI: https://doi.org/10.1134/S0012266119010087
- ID: 154922
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Abstract
We study the extremals of problems of the classical calculus of variations. We obtain a new necessary condition for a strong minimum under the assumption that the Weierstrass and Legendre conditions degenerate, i.e., are satisfied as equalities, on the extremal under study; this condition is called a generalized Weierstrass condition. We also give a modified condition that is a necessary condition for a weak minimum.
About the authors
A. V. Arutyunov
Lomonosov Moscow State University; Peoples’ Friendship University of Russia; Derzhavin Tambov State University
Author for correspondence.
Email: arutyunov@cs.msu.ru
Russian Federation, Moscow, 119991; Moscow, 117198; Tambov, 392000
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