Point-wise characterizations of limits of planar Sobolev homeomorphisms and their quasi-monotonicity

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Point-wise characterizations of limits of planar Sobolev homeomorphisms and their quasi-monotonicity

Popis výsledku v původním jazyce

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)-&gt; 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.

Název v anglickém jazyce

Point-wise characterizations of limits of planar Sobolev homeomorphisms and their quasi-monotonicity

Popis výsledku anglicky

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)-&gt; 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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2025

Kód důvěrnosti údajů

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

Název periodika

Advances in Calculus of Variations

ISSN

1864-8258

e-ISSN

1864-8266

Svazek periodika

18

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

41

Strana od-do

689-729

Kód UT WoS článku

001454846800001

EID výsledku v databázi Scopus

2-s2.0-105010601389