Operator estimates for non-periodically perforated domains with Dirichlet and nonlinear Robin conditions: vanishing limit

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F62690094%3A18470%2F23%3A50020477" target="_blank" >RIV/62690094:18470/23:50020477 - isvavai.cz</a>

Výsledek na webu

<a href="https://link.springer.com/article/10.1007/s13324-022-00765-8" target="_blank" >https://link.springer.com/article/10.1007/s13324-022-00765-8</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s13324-022-00765-8" target="_blank" >10.1007/s13324-022-00765-8</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Operator estimates for non-periodically perforated domains with Dirichlet and nonlinear Robin conditions: vanishing limit

Popis výsledku v původním jazyce

We consider a general second order linear elliptic equation in a finely perforated domain. The shapes of cavities and their distribution in the domain are arbitrary and non-periodic; they are supposed to satisfy minimal natural geometric conditions. On the boundaries of the cavities we impose either the Dirichlet or a nonlinear Robin condition; the choice of the type of the boundary condition for each cavity is arbitrary. Then we suppose that for some cavities the nonlinear Robin condition is sign-definite in certain sense. Provided such cavities and ones with the Dirichlet condition are distributed rather densely in the domain and the characteristic sizes of the cavities and the minimal distances between the cavities satisfy certain simple condition, we show that a solution to our problem tends to zero as the perforation becomes finer. Our main result are order sharp estimates for the L-2- and W-2(1)-norms of the solution uniform in the L-2-norm of the right hand side in the equation.

Název v anglickém jazyce

Operator estimates for non-periodically perforated domains with Dirichlet and nonlinear Robin conditions: vanishing limit

Popis výsledku anglicky

We consider a general second order linear elliptic equation in a finely perforated domain. The shapes of cavities and their distribution in the domain are arbitrary and non-periodic; they are supposed to satisfy minimal natural geometric conditions. On the boundaries of the cavities we impose either the Dirichlet or a nonlinear Robin condition; the choice of the type of the boundary condition for each cavity is arbitrary. Then we suppose that for some cavities the nonlinear Robin condition is sign-definite in certain sense. Provided such cavities and ones with the Dirichlet condition are distributed rather densely in the domain and the characteristic sizes of the cavities and the minimal distances between the cavities satisfy certain simple condition, we show that a solution to our problem tends to zero as the perforation becomes finer. Our main result are order sharp estimates for the L-2- and W-2(1)-norms of the solution uniform in the L-2-norm of the right hand side in the equation.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

<a href="/cs/project/GA22-18739S" target="_blank" >GA22-18739S: Asymptotická a spektrální analýza operátorů v matematické fyzice</a><br>

Návaznosti

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

Rok uplatnění

2023

Kód důvěrnosti údajů

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

Název periodika

Analysis and Mathematical Physics

ISSN

1664-2368

e-ISSN

1664-235X

Svazek periodika

13

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

CH - Švýcarská konfederace

Počet stran výsledku

34

Strana od-do

"Article Number: 5"

Kód UT WoS článku

000889746200001

EID výsledku v databázi Scopus

2-s2.0-85142723111