Pointwise Inequalities for Sobolev Functions on Outward Cuspidal Domains

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F44555601%3A13440%2F22%3A43896260" target="_blank" >RIV/44555601:13440/22:43896260 - isvavai.cz</a>
Result on the web
<a href="https://academic.oup.com/imrn/advance-article-abstract/doi/10.1093/imrn/rnaa279/5999064?redirectedFrom=fulltext" target="_blank" >https://academic.oup.com/imrn/advance-article-abstract/doi/10.1093/imrn/rnaa279/5999064?redirectedFrom=fulltext</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1093/imrn/rnaa279" target="_blank" >10.1093/imrn/rnaa279</a>

Result language
angličtina
Original language name
Pointwise Inequalities for Sobolev Functions on Outward Cuspidal Domains
Original language description
Optimal definitions for Sobolev spaces are crucial in analysis. It was a remarkable discovery of Hajlasz [3] that distributionally defined Sobolev functions can be characterized using pointwise estimates in the context of Sobolev extension domains. This, in part, has played a crucial role in defining Sobolev spaces for general metric measure spaces. Here, we show that for certain cuspidal domains the pointwise characterization holds without any additional assumptions. These domains do not admit extensions for Sobolev functions. Given a domain Rn, we denote by W1,p(), 1 = p = 8, the usual 1st-order Sobolev space consisting of all functions u Lp whose 1st-order.
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
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

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

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