General second order conditions for extrema of functionals
Mahouton Norbert Hounkonnou, Pascal Dkengne Sielenou
TL;DR
This paper establishes comprehensive second order conditions for identifying extrema in variational problems involving higher order Lagrangians with multi-valued functions, using finite dimensional jet space analysis.
Contribution
It provides necessary and sufficient second order conditions for extrema in complex variational problems, extending existing theory to higher order and multi-valued functions.
Findings
Derived necessary second order conditions for extrema.
Proved sufficient second order conditions for variational problems.
Applied finite dimensional jet space framework for analysis.
Abstract
We prove both necessary and sufficient second order conditions of extrema for variational problems involving any higher order continuously twice differentiable Lagrangians with multi-valued dependent functions of several variables. Our analysis is performed in the framework of the finite dimensional total jet space.
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Taxonomy
TopicsNonlinear Partial Differential Equations · Advanced Mathematical Modeling in Engineering · Contact Mechanics and Variational Inequalities