Minimal extension for the α-Manhattan norm
Campbell, D., Kauranen, A., & Radici, E. (2023). Minimal extension for the α-Manhattan norm. Rendiconti Lincei: Matematica e Applicazioni, 34(4), 773-807. https://doi.org/10.4171/rlm/1027
Julkaistu sarjassa
Rendiconti Lincei: Matematica e ApplicazioniPäivämäärä
2023Tekijänoikeudet
© 2024 Accademia Nazionale dei Lincei
Let ∂Q be the boundary of a convex polygon in R2, eα=(cosα,sinα) and eα⊥=(−sinα,cosα) a basis of R2 for some α∈[0,2π) and φ:∂Q→R2 a continuous, finitely piecewise linear injective map. We construct a finitely piecewise affine homeomorphism v:Q→R2 coinciding with φ on ∂Q such that the following property holds: ∣⟨Dv,eα⟩∣(Q) (resp., ⟨Dv,eα⊥⟩∣(Q)) is as close as we want to inf∣⟨Du,eα⟩∣(Q) (resp., inf∣⟨Du,eα⊥⟩∣(Q)) where the infimum is meant over the class of all BV homeomorphisms u extending φ 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.
Julkaisija
European Mathematical Society - EMS - Publishing House GmbHISSN Hae Julkaisufoorumista
1120-6330Asiasanat
Julkaisu tutkimustietojärjestelmässä
https://converis.jyu.fi/converis/portal/detail/Publication/202018689
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Lisätietoja rahoituksesta
The first author was supported by the grant GACR 20-19018Y.Lisenssi
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