Strong approximation of special functions of bounded variation functions with prescribed jump direction

In this note, we show that special functions of bounded variation (SBV)$\mathrm{SBV)}$ functions with jump normal lying in a prescribed set of directions N$\mathcal {N}$ can be approximated by sequences of SBV$\mathrm{SBV}$ functions whose jump set is essentially closed, polyhedral, and preserves th...

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Veröffentlicht in:	Mathematische Nachrichten 2025-01, Vol.298 (1), p.312-327
Hauptverfasser:	Lazzaroni, Giuliano, Wozniak, Piotr, Zeppieri, Caterina Ida
Format:	Artikel
Sprache:	eng
Schlagworte:	Anisotropy Approximation Free‐discontinuity problems Orthogonality Prescribed jump direction SBV‐functions
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description	In this note, we show that special functions of bounded variation (SBV)$\mathrm{SBV)}$ functions with jump normal lying in a prescribed set of directions N$\mathcal {N}$ can be approximated by sequences of SBV$\mathrm{SBV}$ functions whose jump set is essentially closed, polyhedral, and preserves the orthogonality to N$\mathcal {N}$, moreover the functions are smooth away from their jump set.
doi_str_mv	10.1002/mana.202300346
format	Article
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subjects	Anisotropy Approximation Free‐discontinuity problems Orthogonality Prescribed jump direction SBV‐functions
title	Strong approximation of special functions of bounded variation functions with prescribed jump direction
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