On uniform estimates for Laplace equation in balls with small holes
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F16%3A10334338" target="_blank" >RIV/00216208:11320/16:10334338 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1007/s00526-016-1055-y" target="_blank" >http://dx.doi.org/10.1007/s00526-016-1055-y</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00526-016-1055-y" target="_blank" >10.1007/s00526-016-1055-y</a>
Alternative languages
Result language
angličtina
Original language name
On uniform estimates for Laplace equation in balls with small holes
Original language description
In this paper, we consider the Dirichlet problem of the three-dimensional Laplace equation in the unit ball with a shrinking hole. The problem typically arises from homogenization problems in domains perforated with tiny holes. We give an almost complete description concerning the uniform W-1,W- p estimates: for any 3/2 < p < 3 there hold the uniform W-1,W- p estimates; for any 1 < p < 3/ 2 or 3 < p < 8, there are counterexamples indicating that the uniform W-1,W- p estimates do not hold. The results can be generalized to higher dimensions.
Czech name
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Czech description
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Classification
Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Result continuities
Project
<a href="/en/project/LL1202" target="_blank" >LL1202: Implicitly constituted material models: from theory through model reduction to efficient numerical methods</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2016
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Calculus of Variations and Partial Differential Equations
ISSN
0944-2669
e-ISSN
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Volume of the periodical
55
Issue of the periodical within the volume
5
Country of publishing house
US - UNITED STATES
Number of pages
19
Pages from-to
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UT code for WoS article
000386708700002
EID of the result in the Scopus database
2-s2.0-84988358556