caa a22 4500 606233318 CHVBK 20210128101231.0 cr unu---uuuuu 210128e20150701xx s 000 0 eng 10.1007/s10883-014-9231-x doi (NATIONALLICENCE)springer-10.1007/s10883-014-9231-x Fréchet Generalized Trajectories and Minimizers for Variational Problems of Low Coercivity [Elektronische Daten] [Manuel Guerra, Andrey Sarychev] We address consecutively two problems. First, we introduce a class of so-called Fréchet generalized controls for a multi-input control-affine system with non-commuting controlled vector fields. For each control of the class, one is able to define a unique generalized trajectory, and the input-to-trajectory map turns out to be continuous with respect to the Fréchet metric. On the other side, the class of generalized controls is broad enough to settle the second problem, which is to prove existence of generalized minimizers of Lagrange variational problem with functionals of low (in particular linear) growth. Besides, we study the possibility of Lavrentiev-type gap between the infima of the functionals in the spaces of ordinary and generalized controls. This is an abridged (due to the journal space limitations) version of a more detailed preprint with several proofs, drawings, and examples added, published in arXiv.org > math > arXiv: 1402.0477 . Springer Science+Business Media New York, 2014 Generalized controls nationallicence Impulsive controls nationallicence Non-involutive systems nationallicence Existence of minimizers nationallicence Lavrentiev phenomenon nationallicence Guerra Manuel CEMAPRE, University of Lisbon, Lisbon, Portugal aut Sarychev Andrey ISEG, University of Lisbon, Lisbon, Portugal aut Journal of Dynamical and Control Systems Springer US; http://www.springer-ny.com 21/3(2015-07-01), 351-377 1079-2724 21:3<351 2015 21 10883 https://doi.org/10.1007/s10883-014-9231-x text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10883-014-9231-x text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Guerra Manuel CEMAPRE, University of Lisbon, Lisbon, Portugal aut NATIONALLICENCE 700 1- Sarychev Andrey ISEG, University of Lisbon, Lisbon, Portugal aut NATIONALLICENCE 773 0- Journal of Dynamical and Control Systems Springer US; http://www.springer-ny.com 21/3(2015-07-01), 351-377 1079-2724 21:3<351 2015 21 10883