| Issue |
ESAIM: COCV
Volume 20, Number 4, October-December 2014
|
|
|---|---|---|
| Page(s) | 1153 - 1180 | |
| DOI | https://doi.org/10.1051/cocv/2014010 | |
| Published online | 08 August 2014 | |
Nonsmooth Problems of Calculus of Variations via Codifferentiation∗
Faculty of Applied Mathematics and Control Processes, Saint
Petersburg State University, Petergof, 198504
Saint Petersburg,
Russia
This email address is being protected from spambots. You need JavaScript enabled to view it.
Received: 16 November 2012
Revised: 18 January 2014
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.
Mathematics Subject Classification: 49K10 / 90C30
Key words: Nonsmooth analysis / calculus of variations / codifferentiable function / problem of Bolza
The work was financially supported by the Russian Foundation for Basic Research (Grant No. 12–01–00752).
© EDP Sciences, SMAI, 2014
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