On elliptic operators with Steklov condition perturbed by Dirichlet condition on a small part of boundary

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

On elliptic operators with Steklov condition perturbed by Dirichlet condition on a small part of boundary

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

On elliptic operators with Steklov condition perturbed by Dirichlet condition on a small part of boundary

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2021

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS

ISSN

0944-2669

e-ISSN

—

Svazek periodika

60

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

44

Strana od-do

"Article Number: 48"

Kód UT WoS článku

000614436100001

EID výsledku v databázi Scopus

2-s2.0-85100394689