Classification of strict limits of planar BV homeomorphisms

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F62690094%3A18470%2F23%3A50020438" target="_blank" >RIV/62690094:18470/23:50020438 - isvavai.cz</a>

Výsledek na webu

<a href="https://www.sciencedirect.com/science/article/pii/S0022123623001106?via%3Dihub" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0022123623001106?via%3Dihub</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.jfa.2023.109953" target="_blank" >10.1016/j.jfa.2023.109953</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Classification of strict limits of planar BV homeomorphisms

Popis výsledku v původním jazyce

We present a classification of m-strict limits (i.e. fk (*)-&gt; f and *|D1f(k)|(Omega) + |D(2)f(k)|(Omega) -&gt; |D(1)f |(Omega) + |D(2)f |(Omega)) of planar BV homeomorphisms; a class previously studied by the authors and S. Hencl in [6]. There it was shown that such mappings allow for cavitations and fractures singularities but fulfil a suitable generalization of the INV condition. As pointed out by J. Ball [3], these features are physically expected by limit configurations of elastic deformations. In the present work we develop a suitable generalization of the no-crossing condition introduced by De Philippis and Pratelli in [8] to describe weak limits of planar Sobolev homeomorphisms that we call the no -crossing BV condition, and we show that a planar mapping satisfies this property if and only if it can be approximated m-strictly by homeomorphisms of bounded variations. (c) 2023 Elsevier Inc. All rights reserved.

Název v anglickém jazyce

Classification of strict limits of planar BV homeomorphisms

Popis výsledku anglicky

We present a classification of m-strict limits (i.e. fk (*)-&gt; f and *|D1f(k)|(Omega) + |D(2)f(k)|(Omega) -&gt; |D(1)f |(Omega) + |D(2)f |(Omega)) of planar BV homeomorphisms; a class previously studied by the authors and S. Hencl in [6]. There it was shown that such mappings allow for cavitations and fractures singularities but fulfil a suitable generalization of the INV condition. As pointed out by J. Ball [3], these features are physically expected by limit configurations of elastic deformations. In the present work we develop a suitable generalization of the no-crossing condition introduced by De Philippis and Pratelli in [8] to describe weak limits of planar Sobolev homeomorphisms that we call the no -crossing BV condition, and we show that a planar mapping satisfies this property if and only if it can be approximated m-strictly by homeomorphisms of bounded variations. (c) 2023 Elsevier Inc. All rights reserved.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GJ20-19018Y" target="_blank" >GJ20-19018Y: Jemné analytické a topologické metody pro variační problémy a modelování</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2023

Kód důvěrnosti údajů

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

Název periodika

Journal of functional analysis

ISSN

0022-1236

e-ISSN

1096-0783

Svazek periodika

285

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

30

Strana od-do

"Article Number: 109953"

Kód UT WoS článku

000983585300001

EID výsledku v databázi Scopus

2-s2.0-85152683099