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Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2015, Volume 15, Issue 4, Pages 422–432
DOI: https://doi.org/10.18500/1816-9791-2015-15-4-422-432
(Mi isu610)
 

Mathematics

Dominant integrands growth estimates and smoothness of variational functionals in Sobolev spaces

I. V. Orlov, I. A. Romanenko

V. I. Vernadsky Crimean Federal University, 4, Vernadskogo ave., 295007, Simferopol, Republic of Crimea, Russia
References:
Abstract: For variational functionals in Sobolev spaces $\{W^{1,p}\}\;(1\leq p<\infty)$ we introduce a sequence of so-called dominant “growth estimates” for the gradient of appropriate order of the integrand, each of which guarantees the appropriate level of smoothness of variational functional in the $C^{1}$-smooth points of the Sobolev space. Earlier studied K-pseudopolynomial representations of the integrand are particular cases of dominant growth estimates. However, unlike the pseudopolynomial case $(p\in \mathbb{N})$, our approach enables us to consider variational problems on the complete Sobolev scale $(1\leq p<\infty)$.
Key words: variational functional, Sobolev spaces, integrant, dominant growth estimates, dominating mixed smoothness, variational problems.
Funding agency Grant number
Russian Foundation for Basic Research 15-41-01005
The results of the first author were obtained by the financial support of Regional Grant of the Russian Foundation for Basic Research (project no. 15-41-01005).
Bibliographic databases:
Document Type: Article
UDC: 517.972:517.98:517.982
Language: Russian
Citation: I. V. Orlov, I. A. Romanenko, “Dominant integrands growth estimates and smoothness of variational functionals in Sobolev spaces”, Izv. Saratov Univ. Math. Mech. Inform., 15:4 (2015), 422–432
Citation in format AMSBIB
\Bibitem{OrlRom15}
\by I.~V.~Orlov, I.~A.~Romanenko
\paper Dominant integrands growth estimates and smoothness of variational functionals in Sobolev spaces
\jour Izv. Saratov Univ. Math. Mech. Inform.
\yr 2015
\vol 15
\issue 4
\pages 422--432
\mathnet{http://mi.mathnet.ru/isu610}
\crossref{https://doi.org/10.18500/1816-9791-2015-15-4-422-432}
\elib{https://elibrary.ru/item.asp?id=25360658}
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    Известия Саратовского университета. Новая серия. Серия Математика. Механика. Информатика
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