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Tr. Mosk. Mat. Obs., 2014, Volume 75, Issue 2, Pages 139–157 (Mi mmo561)  

Comparison of the singular numbers of correct restrictions of elliptic differential operators

V. I. Burenkova, M. Otelbaevb

a Faculty of Natural Sciences, Peoples’ Friendship University of Russia, Moscow, Russia
b Faculty of Mechanics and Mathematics, L. N. Gumilyov Eurasian National University, Astana, Kazakhstan

Abstract: The paper is dedicated to finding the asymptotics of singular numbers of a correct restriction of a uniformly elliptic differential operator of order $2l$ defined on a bounded domain in $\mathbb{R}^n$ with sufficiently smooth boundary, which is in general a non-selfadjoint operator. Conditions are established on a correct restriction, ensuring that its singular numbers $s_k$ are of order $k^{2l/n}$ as $k\to\infty$. As an application of this result certain estimates are obtained for the deviation upon domain perturbation of singular numbers of such correct restrictions.
References: 12 entries.

Key words and phrases: correct restrictions of operators, leading and non-leading operators, estimates and asymptotics for singular numbers, spectral stability estimates.

Funding Agency Grant Number
Russian Science Foundation 14-11-00443
V. I. Burenkov’s research was supported by a grant from the Russian Scientific Foundation (project 14-11-00443).


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English version:
Transactions of the Moscow Mathematical Society, 2014, 75, 115–131

UDC: 517.956, 517.984
MSC: 35P15, 35P20, 35J40, 47A75
Received: 02.02.2014
Language:

Citation: V. I. Burenkov, M. Otelbaev, “Comparison of the singular numbers of correct restrictions of elliptic differential operators”, Tr. Mosk. Mat. Obs., 75, no. 2, MCCME, M., 2014, 139–157; Trans. Moscow Math. Soc., 75 (2014), 115–131

Citation in format AMSBIB
\Bibitem{BurOte14}
\by V.~I.~Burenkov, M.~Otelbaev
\paper Comparison of the singular numbers of correct restrictions of elliptic differential operators
\serial Tr. Mosk. Mat. Obs.
\yr 2014
\vol 75
\issue 2
\pages 139--157
\publ MCCME
\publaddr M.
\mathnet{http://mi.mathnet.ru/mmo561}
\elib{http://elibrary.ru/item.asp?id=23780160}
\transl
\jour Trans. Moscow Math. Soc.
\yr 2014
\vol 75
\pages 115--131
\crossref{https://doi.org/10.1090/S0077-1554-2014-00229-6}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84960118995}


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