Point-wise characterizations of limits of planar Sobolev homeomorphisms and their quasi-monotonicity
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F25%3A10512294" target="_blank" >RIV/00216208:11320/25:10512294 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=5uVVBXSqQP" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=5uVVBXSqQP</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1515/acv-2024-0043" target="_blank" >10.1515/acv-2024-0043</a>
Alternative languages
Result language
angličtina
Original language name
Point-wise characterizations of limits of planar Sobolev homeomorphisms and their quasi-monotonicity
Original language description
We present three novel classifications of the weak sequential (and strong) limits in W-1,W-p of planar diffeomorphisms. We introduce a concept called the QM condition which is a kind of separation property for pre-images of closed connected sets and show that u satisfies this property exactly when it is the limit of Sobolev homeomorphisms. Further, we prove that u is an element of W-id(1,p)((-1,1)(2),R-2) is the limit of a sequence of homeomorphisms exactly when there are classically monotone mappings g(delta ): [-1,1](2)-> R-2 and very small open sets U-delta such that g(delta )= u on [-1,1](2)U-delta. Also, we introduce the so-called three curve condition, which is in some sense reminiscent of the NCL condition of but for u(-1) instead of for u, and prove that a map is the W-1,W-p limit of planar Sobolev homeomorphisms exactly when it satisfies this property.
Czech name
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Czech description
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Classification
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
Result continuities
Project
—
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Advances in Calculus of Variations
ISSN
1864-8258
e-ISSN
1864-8266
Volume of the periodical
18
Issue of the periodical within the volume
3
Country of publishing house
DE - GERMANY
Number of pages
41
Pages from-to
689-729
UT code for WoS article
001454846800001
EID of the result in the Scopus database
2-s2.0-105010601389