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

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61389005%3A_____%2F22%3A00561934" target="_blank" >RIV/61389005:_____/22:00561934 - isvavai.cz</a>
Alternative codes found
RIV/62690094:18470/22:50019457
Result on the web
<a href="https://doi.org/10.1016/j.jde.2022.08.005" target="_blank" >https://doi.org/10.1016/j.jde.2022.08.005</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jde.2022.08.005" target="_blank" >10.1016/j.jde.2022.08.005</a>

Result language
angličtina
Original language name
Operator estimates for homogenization of the Robin Laplacian in a perforated domain
Original language description
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.
Czech name
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Czech description
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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
10101 - Pure mathematics

Project
<a href="/en/project/GA21-07129S" target="_blank" >GA21-07129S: New Effects from Time-Reversal Non-Invariance</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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