Elliptic Operators in Multidimensional Cylinders with Frequently Alternating Boundary Conditions Along a Given Curve

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F62690094%3A18470%2F20%3A50017100" target="_blank" >RIV/62690094:18470/20:50017100 - isvavai.cz</a>

Result on the web

<a href="https://link.springer.com/article/10.1007/s10958-019-04624-z" target="_blank" >https://link.springer.com/article/10.1007/s10958-019-04624-z</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s10958-019-04624-z" target="_blank" >10.1007/s10958-019-04624-z</a>

Result language

angličtina

Original language name

Elliptic Operators in Multidimensional Cylinders with Frequently Alternating Boundary Conditions Along a Given Curve

Original language description

We consider a selfadjoint elliptic operator in an infinite multidimensional cylinder with the Dirichlet boundary condition which is replaced by the Robin condition on small sets located along a given line on the boundary. The shape and distribution of these sets are arbitrary. The characteristic linear size of these sets is a small parameter of the problem. It is shown that the resolvent of such an operator converges to the resolvent of the homogenized operator, and an estimate for the convergence rate is obtained. The homogenized operator is the same operator, but without alternating boundary conditions. The difference of resolvents is estimated in the norm of bounded operators acting from L2 to W21. If the small sets are periodically distributed and have the same shape and the Robin condition is replaced by the Neumann condition, we derive two-sided asymptotic estimates for the lower band functions, which provides the possibility to estimate from below the length of the first band of the spectrum.

Czech name

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Czech description

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Type

J_SC - Article in a specialist periodical, which is included in the SCOPUS database

CEP classification

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OECD FORD branch

10102 - Applied mathematics

Project

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Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2020

Confidentiality

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

Name of the periodical

Journal of mathematical sciences

ISSN

1072-3374

e-ISSN

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Volume of the periodical

244

Issue of the periodical within the volume

3

Country of publishing house

US - UNITED STATES

Number of pages

12

Pages from-to

378-389

UT code for WoS article

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EID of the result in the Scopus database

2-s2.0-85076917754