Constrained variational problems governed by second-order Lagrangians

ABSTRACT

In this paper, the analysis is focused on the optimization of some simple, multiple or curvilinear integral functionals (governed by second-order Lagrangians) subject to ODEs, PDEs or isoperimetric constraints. In this context, using appropriate techniques of calculus of variations and some geometric tools, necessary conditions of optimality are formulated. As well, the theory developed in this paper is illustrated with applications.

Keywords:

• Multi-time
• Lagrangian
• Euler-Lagrange equations
• isoperimetric constraints
• differential 1-form

AMS subject classifications:

• 49K15
• 49K20
• 49K21
• 65K10

Disclosure statement

No potential conflict of interest was reported by the authors.