Extremum conditions for functionals involving higher derivatives of several variable vector valued functions

2011/07/26 by Mahouton Norbert Hounkonnou, Hounkonnou, Mahouton Norbert, Pascal Dkengne Sielenou +1
Computer Science · Engineering · #35A15 #35A40 #49-01 #49J10 #49J40 #Composite Structure Analysis and Optimization #Contact Mechanics and Variational Inequalities #Dynamics and Control of Mechanical Systems #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · pdf · doi:10.48550/arxiv.1107.5344

openalex publication_date 2011/07/26 · openalex created_date 2022/08/29 · openalex updated_date 2026/07/28

Abstract

This paper addresses both necessary and relevant sufficient extremum conditions for a variational problem defined by a smooth Lagrangian, involving higher derivatives of several variable vector valued functions. A general formulation of first order necessary extremum conditions for variational problems with (or without) constraints is given. Global Legendre second order necessary extremum conditions are provided as well as new general explicit formula for second order sufficient extremum condition which does not require the notion of conjugate points as in the Jacobi sufficient condition.

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