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
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.
|Russian Science Foundation
|The research of I.V. Orlov was supported by the Russian Scientific Foundation (project 14-21-00066, Voronezh State Uniersity).
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MSC: 49J05, 49L99
I. V. Orlov, A. V. Tsygankova, “Multidimensional variational functionals with subsmooth integrands”, Eurasian Math. J., 6:3 (2015), 54–75
Citation in format AMSBIB
\by I.~V.~Orlov, A.~V.~Tsygankova
\paper Multidimensional variational functionals with subsmooth integrands
\jour Eurasian Math. J.
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