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Eurasian Math. J., 2015, Volume 6, Number 3, Pages 54–75 (Mi emj202)  

Multidimensional variational functionals with subsmooth integrands

I. V. Orlovab, A. V. Tsygankovaa

a Department of Mathematics and Informatics, Crimea Federal V. Vernadsky University, 4 Academician Vernadsky Avenue, Simferopol, Republic of Crimea, Russia, 295007
b Institute of Mathematics, Voronezh State University, 1 University Square, Voronezh, Russia, 394006

Abstract: In the present paper, we establish a base of investigation of multidimensional variational functionals having $C^1$-subsmooth or $C^2$-subsmooth integrands. First, an estimate of the first $K$-variation for the multidimensional variational functional having a $C^1$-subsmooth integrand is obtained and numerous partial cases are studied. Secondly, we have obtained $C^1$-subsmooth generalizations of the basic variational lemma and Euler–Ostrogradskii equation. Finally, for the $C^2$-subsmooth case, an estimate of the second $K$-variational is obtained and a series of the partial cases is studied as well.

Keywords and phrases: compact subdifferential, subsmoothness, multidimensional variational functional, Euler–Ostrogradskii equation, Euler–Ostrogradskii inclusion.

Funding Agency Grant Number
Russian Science Foundation 14-21-00066
The research of I.V. Orlov was supported by the Russian Scientific Foundation (project 14-21-00066, Voronezh State Uniersity).


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Bibliographic databases:
MSC: 49J05, 49L99
Received: 31.01.2015
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Citation: I. V. Orlov, A. V. Tsygankova, “Multidimensional variational functionals with subsmooth integrands”, Eurasian Math. J., 6:3 (2015), 54–75

Citation in format AMSBIB
\Bibitem{OrlTsy15}
\by I.~V.~Orlov, A.~V.~Tsygankova
\paper Multidimensional variational functionals with subsmooth integrands
\jour Eurasian Math. J.
\yr 2015
\vol 6
\issue 3
\pages 54--75
\mathnet{http://mi.mathnet.ru/emj202}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000374499900005}


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