Minimal extension for the a-Manhattan norm

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F23%3A10493143" target="_blank" >RIV/00216208:11320/23:10493143 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=DJHhS.FbB2" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=DJHhS.FbB2</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.4171/RLM/1027" target="_blank" >10.4171/RLM/1027</a>

Result language
angličtina
Original language name
Minimal extension for the a-Manhattan norm
Original language description
Let partial derivative Q be the boundary of a convex polygon in R-2, e(alpha) = (cos alpha, sin alpha) and e(alpha)(perpendicular to) = (- sin alpha, cos alpha) a basis of R-2 for some alpha is an element of [0, 2 pi) and phi : partial derivative Q -> R-2 a continuous, finitely piecewise linear injective map. We construct a finitely piecewise affine homeomorphism v : Q -> R-2 coinciding with phi on partial derivative Q such that the following property holds: l(D-u, e(alpha))l(Q) (resp., (Du, e(alpha)(perpendicular to))l(Q)) is as close as we want to inf l(D-u, e(alpha))l(Q) (resp., inf l(Du, e(alpha)(perpendicular to))l(Q)) where the infimum is meant over the class of all BV homeomorphisms u extending phi inside Q. This result extends that already proven by Pratelli and the third author in [Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl. 29 (2018), no. 3, 511-555] in the shape of the domain.
Czech name
—
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
—
OECD FORD branch
10101 - Pure mathematics

Project
—
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

Name of the periodical
Atti della Accademia Nazionale dei Lincei, Classe di Scienze Fisiche, Matematiche e Naturali, Rendiconti Lincei Matematica E Applicazioni
ISSN
1120-6330
e-ISSN
1720-0768
Volume of the periodical
34
Issue of the periodical within the volume
4
Country of publishing house
IT - ITALY
Number of pages
35
Pages from-to
773-807
UT code for WoS article
001177573000002
EID of the result in the Scopus database
2-s2.0-85186757443

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