Higher-order Sobolev embeddings and isoperimetric inequalities

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F15%3A10317035" target="_blank" >RIV/00216208:11320/15:10317035 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1016/j.aim.2014.12.027" target="_blank" >http://dx.doi.org/10.1016/j.aim.2014.12.027</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.aim.2014.12.027" target="_blank" >10.1016/j.aim.2014.12.027</a>

Result language
angličtina
Original language name
Higher-order Sobolev embeddings and isoperimetric inequalities
Original language description
Optimal higher-order Sobolev type embeddings are shown to follow via isoperimetric inequalities. This establishes a higher-order analogue of a well-known link between first-order Sobolev embeddings and isoperimetric inequalities. Sobolev type inequalities of any order, involving arbitrary rearrangement-invariant norms, on open sets in Rn, possibly endowed with a measure density, are reduced to much simpler one-dimensional inequalities for suitable integral operators depending on the isoperimetric function of the relevant sets. As a consequence, the optimal target space in the relevant Sobolev embeddings can be determined both in standard and in non-standard classes of function spaces and underlying measure spaces.
Czech name
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Czech description
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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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Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
S - Specificky vyzkum na vysokych skolach<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2015
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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