DIMENSION DISTORTION OF IMAGES OF SETS UNDER SOBOLEV MAPPINGS

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F15%3A10314060" target="_blank" >RIV/00216208:11320/15:10314060 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.5186/aasfm.2015.4026" target="_blank" >http://dx.doi.org/10.5186/aasfm.2015.4026</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.5186/aasfm.2015.4026" target="_blank" >10.5186/aasfm.2015.4026</a>

Result language
angličtina
Original language name
DIMENSION DISTORTION OF IMAGES OF SETS UNDER SOBOLEV MAPPINGS
Original language description
Let f: R-n -> R-k be a continuous representative of a mapping in a Sobolev space W-1,W-P, p > n. Suppose that the Hausdorff dimension of a set M is at most alpha. Kaufmann [12] proved an optimal bound beta = p alpha/p-n+alpha for the dimension of the image of M under the mapping f. We show that this bound remains essentially valid even for 1 < p {= n and we also prove analogous bound for mappings in Sobolev spaces with higher order or even fractional smoothness.
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
—

Project
<a href="/en/project/LL1203" target="_blank" >LL1203: Properties of functions and mappings in Sobolev spaces</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

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

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