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Nonsmooth Problems of Calculus of Variations via Codifferentiation

Published online by Cambridge University Press:  08 August 2014

Maxim Dolgopolik*
Affiliation:
Faculty of Applied Mathematics and Control Processes, Saint Petersburg State University, Petergof, 198504 Saint Petersburg, Russia. maxim.dolgopolik@gmail.com
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Abstract

In this paper multidimensional nonsmooth, nonconvex problems of the calculus of variations with codifferentiable integrand are studied. Special classes of codifferentiable functions, that play an important role in the calculus of variations, are introduced and studied. The codifferentiability of the main functional of the calculus of variations is derived. Necessary conditions for the extremum of a codifferentiable function on a closed convex set and its applications to the nonsmooth problems of the calculus of variations are described. Necessary optimality conditions in the main problem of the calculus of variations and in the problem of Bolza in the nonsmooth case are derived. Examples comparing presented results with other approaches to nonsmooth problems of the calculus of variations are given.

Type
Research Article
Copyright
© EDP Sciences, SMAI, 2014

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