This article is cited in 1 paper

Multidimensional variational functionals with subsmooth integrands

I. V. Orlov^ab, A. V. Tsygankova<sup>a

a</sup> 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.

MSC: 49J05, 49L99

Received: 31.01.2015

Language: English

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