Weak Limit of Homeomorphisms in W1,n-1 and (INV) Condition

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F23%3A10475521" target="_blank" >RIV/00216208:11320/23:10475521 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=UNnHqUgH3A" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=UNnHqUgH3A</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00205-023-01911-7" target="_blank" >10.1007/s00205-023-01911-7</a>

Result language
angličtina
Original language name
Weak Limit of Homeomorphisms in W1,n-1 and (INV) Condition
Original language description
Let Omega, Omega' subset of R-3 be Lipschitz domains, let f(m) : Omega -> Omega' be a sequence of homeomorphisms with prescribed Dirichlet boundary condition and sup(m) integral(Omega) (|D integral(m)|(2) + 1/J(fm)(2)) < infinity. Let f be a weak limit of f(m) in W-1,W-2. We show that f is invertible a.e., and more precisely that it satisfies the (INV) condition of Conti and De Lellis, and thus that it has all of the nice properties of mappings in this class. Generalization to higher dimensions and an example showing sharpness of the condition 1/J(f)(2) is an element of L-1 are also given. Using this example we also show that, unlike the planar case, the class of weak limits and the class of strong limits of W-1,W-2 Sobolev homeomorphisms in R-3 are not the same.
Czech name
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Czech description
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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

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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