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DIMENSION DISTORTION OF IMAGES OF SETS UNDER SOBOLEV MAPPINGS

The result's identifiers

  • 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>

Alternative languages

  • 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

  • Czech description

Classification

  • Type

    J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

  • CEP classification

    BA - General mathematics

  • OECD FORD branch

Result continuities

  • 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

Others

  • Publication year

    2015

  • Confidentiality

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

Data specific for result type

  • Name of the periodical

    Annales Academiae Scientiarum Fennicae Mathematica

  • ISSN

    1239-629X

  • e-ISSN

  • Volume of the periodical

    40

  • Issue of the periodical within the volume

    1

  • Country of publishing house

    FI - FINLAND

  • Number of pages

    16

  • Pages from-to

    427-442

  • UT code for WoS article

    000349659000025

  • EID of the result in the Scopus database

    2-s2.0-84921939051