On elliptic operators with Steklov condition perturbed by Dirichlet condition on a small part of boundary
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F62690094%3A18470%2F21%3A50017891" target="_blank" >RIV/62690094:18470/21:50017891 - isvavai.cz</a>
Result on the web
<a href="https://link.springer.com/article/10.1007/s00526-020-01847-w" target="_blank" >https://link.springer.com/article/10.1007/s00526-020-01847-w</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00526-020-01847-w" target="_blank" >10.1007/s00526-020-01847-w</a>
Alternative languages
Result language
angličtina
Original language name
On elliptic operators with Steklov condition perturbed by Dirichlet condition on a small part of boundary
Original language description
We consider a boundary value problem for a homogeneous elliptic equation with an inhomogeneous Steklov boundary condition. The problem involves a singular perturbation, which is the Dirichlet condition imposed on a small piece of the boundary. We rewrite such problem to a resolvent equation for a self-adjoint operator in a fractional Sobolev space on the boundary of the domain. We prove the norm convergence of this operator to a limiting one associated with an unperturbed problem involving no Dirichlet condition. We also establish an order sharp estimate for the convergence rate. The established convergence implies the convergence of the spectra and spectral projectors. In the second part of the work we study perturbed eigenvalues converging to limiting simple discrete ones. We construct two-terms asymptotic expansions for such eigenvalues and for the associated eigenfunctions.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10102 - Applied mathematics
Result continuities
Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS
ISSN
0944-2669
e-ISSN
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Volume of the periodical
60
Issue of the periodical within the volume
1
Country of publishing house
DE - GERMANY
Number of pages
44
Pages from-to
"Article Number: 48"
UT code for WoS article
000614436100001
EID of the result in the Scopus database
2-s2.0-85100394689