The Norm Resolvent Convergence for Elliptic Operators in Multi-Dimensional Domains with Small Holes

The Norm Resolvent Convergence for Elliptic Operators in Multi-Dimensional Domains with Small Holes DOI 10.1007/s10958-018-3873-2 Journal of Mathematical Sciences, Vol. 232, No. 3, July, 2018 THE NORM RESOLVENT CONVERGENCE FOR ELLIPTIC OPERATORS IN MULTI-DIMENSIONAL DOMAINS WITH SMALL HOLES D. I. Borisov Institute of Mathematics, USC RAS 112, Chernyshevskii St., Ufa 450008, Russia Bashkir State Pedagogical University 3a, October Revolution St., Ufa 450000, Russia University of Hradec Kr´ alov´e 62, Rokitansk´eho, Hradec Kr´ alov´e 50003, Czech Republic borisovdi@yandex.ru A. I. Mukhametrakhimova Bashkir State Pedagogical University 3a, October Revolution St., Ufa 450000, Russia albina8558@yandex.ru UDC 517.956+517.958 We consider a second order elliptic operator with variable coefficients in a multi- dimensional domain with a small hole and some classical boundary condition on the hole boundary. We show that the resolvent of this operator converges to the resolvent of the limit operator in the domain without holes in the sense of the norm of bounded operators acting from L to W . For the convergence rate we obtain sharp estimates relative to the smallness order. Bibliography:28 titles. Dedicated to the memory of Vasilii Vasil’evich Zhikov Boundary value problems in domains with small holes are related to the classical theory of singular perturbations. A small hole is one of the simplest examples of a geometric perturbation to http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Mathematical Sciences Springer Journals

The Norm Resolvent Convergence for Elliptic Operators in Multi-Dimensional Domains with Small Holes

Loading next page...
 
/lp/springer_journal/the-norm-resolvent-convergence-for-elliptic-operators-in-multi-9K2C1H7PHn
Publisher
Springer US
Copyright
Copyright © 2018 by Springer Science+Business Media, LLC, part of Springer Nature
Subject
Mathematics; Mathematics, general
ISSN
1072-3374
eISSN
1573-8795
D.O.I.
10.1007/s10958-018-3873-2
Publisher site
See Article on Publisher Site

Abstract

DOI 10.1007/s10958-018-3873-2 Journal of Mathematical Sciences, Vol. 232, No. 3, July, 2018 THE NORM RESOLVENT CONVERGENCE FOR ELLIPTIC OPERATORS IN MULTI-DIMENSIONAL DOMAINS WITH SMALL HOLES D. I. Borisov Institute of Mathematics, USC RAS 112, Chernyshevskii St., Ufa 450008, Russia Bashkir State Pedagogical University 3a, October Revolution St., Ufa 450000, Russia University of Hradec Kr´ alov´e 62, Rokitansk´eho, Hradec Kr´ alov´e 50003, Czech Republic borisovdi@yandex.ru A. I. Mukhametrakhimova Bashkir State Pedagogical University 3a, October Revolution St., Ufa 450000, Russia albina8558@yandex.ru UDC 517.956+517.958 We consider a second order elliptic operator with variable coefficients in a multi- dimensional domain with a small hole and some classical boundary condition on the hole boundary. We show that the resolvent of this operator converges to the resolvent of the limit operator in the domain without holes in the sense of the norm of bounded operators acting from L to W . For the convergence rate we obtain sharp estimates relative to the smallness order. Bibliography:28 titles. Dedicated to the memory of Vasilii Vasil’evich Zhikov Boundary value problems in domains with small holes are related to the classical theory of singular perturbations. A small hole is one of the simplest examples of a geometric perturbation to

Journal

Journal of Mathematical SciencesSpringer Journals

Published: Jun 2, 2018

References

You’re reading a free preview. Subscribe to read the entire article.


DeepDyve is your
personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy affordable access to
over 18 million articles from more than
15,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Search

Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly

Organize

Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.

Access

Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

See the journals in your area

DeepDyve

Freelancer

DeepDyve

Pro

Price

FREE

$49/month
$360/year

Save searches from
Google Scholar,
PubMed

Create lists to
organize your research

Export lists, citations

Read DeepDyve articles

Abstract access only

Unlimited access to over
18 million full-text articles

Print

20 pages / month

PDF Discount

20% off