Operator estimates for homogenization of the Robin Laplacian in a perforated domain

Kód výsledku v IS VaVaI

RIV/61389005:_____/22:00561934 - isvavai.cz

Nalezeny alternativní kódy

RIV/62690094:18470/22:50019457

Výsledek na webu

https://doi.org/10.1016/j.jde.2022.08.005

DOI - Digital Object Identifier

10.1016/j.jde.2022.08.005

Jazyk výsledku

angličtina

Název v původním jazyce

Operator estimates for homogenization of the Robin Laplacian in a perforated domain

Popis výsledku v původním jazyce

Let epsilon > 0 be a small parameter. We consider the domain omega := omega omega epsilon, where omega is an open domain in Rn, and D epsilon is a family of small balls of the radius d epsilon = o(epsilon) distributed periodically with period epsilon. Let ?epsilon be the Laplace operator in ?epsilon subject to the Robin condition partial differential u partial differential n + gamma epsilon u = 0 with gamma epsilon <= 0 on the boundary of the holes and the Dirichlet condition on the exterior boundary. Kaizu (1985, 1989) and Brillard (1988) have shown that, under appropriate assumptions on d epsilon and gamma epsilon, the operator ?epsilon converges in the strong resolvent sense to the sum of the Dirichlet Laplacian in omega and a constant potential. We improve this result deriving estimates on the rate of convergence in terms of L2 -> L2 and L2 -> H1 operator norms. As a byproduct we establish the estimate on the distance between the spectra of the associated operators.(c) 2022 Elsevier Inc. All rights reserved.

Název v anglickém jazyce

Operator estimates for homogenization of the Robin Laplacian in a perforated domain

Popis výsledku anglicky

Let epsilon > 0 be a small parameter. We consider the domain omega := omega omega epsilon, where omega is an open domain in Rn, and D epsilon is a family of small balls of the radius d epsilon = o(epsilon) distributed periodically with period epsilon. Let ?epsilon be the Laplace operator in ?epsilon subject to the Robin condition partial differential u partial differential n + gamma epsilon u = 0 with gamma epsilon <= 0 on the boundary of the holes and the Dirichlet condition on the exterior boundary. Kaizu (1985, 1989) and Brillard (1988) have shown that, under appropriate assumptions on d epsilon and gamma epsilon, the operator ?epsilon converges in the strong resolvent sense to the sum of the Dirichlet Laplacian in omega and a constant potential. We improve this result deriving estimates on the rate of convergence in terms of L2 -> L2 and L2 -> H1 operator norms. As a byproduct we establish the estimate on the distance between the spectra of the associated operators.(c) 2022 Elsevier Inc. All rights reserved.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

GA21-07129S: Nové jevy pocházející z narušení invariance vůči časové inversi

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2022

Kód důvěrnosti údajů

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

Název periodika

Journal of Differential Equations

ISSN

0022-0396

e-ISSN

1090-2732

Svazek periodika

338

Číslo periodika v rámci svazku

NOV

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

44

Strana od-do

474-517

Kód UT WoS článku

000859448200002

EID výsledku v databázi Scopus

2-s2.0-85136559022