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


Authors: V. I. Burenkov and M. Otelbaev
Original publication: Trudy Moskovskogo Matematicheskogo Obshchestva, tom 75 (2014), vypusk 2.
Journal: Trans. Moscow Math. Soc. 2014, 115-131
MSC (2010): Primary 35P15, 35P20, 35J40, 47A75
DOI: https://doi.org/10.1090/S0077-1554-2014-00229-6
Published electronically: November 4, 2014
MathSciNet review: 3308605
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Abstract | References | Similar Articles | Additional Information

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.


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Additional Information

V. I. Burenkov
Affiliation: Faculty of Natural Sciences, People’s Friendship University of Russia, Moscow, Russia
Email: burenkov@cf.ac.uk

M. Otelbaev
Affiliation: Faculty of Mechanics and Mathematics, L. N. Gumilyov Eurasian National University, Astana, Kazakhstan
Email: otelbaevm@mail.ru

DOI: https://doi.org/10.1090/S0077-1554-2014-00229-6
Keywords: Correct restrictions of operators, leading and non-leading operators, estimates and asymptotics for singular numbers, spectral stability estimates
Published electronically: November 4, 2014
Additional Notes: V. I. Burenkov’s research was supported by a grant from the Russian Scientific Foundation (project 14-11-00443).
Article copyright: © Copyright 2014 V. I. Burenkov and M. Otelbaev

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