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

Giuliano Lazzaroni, Piotr Wozniak and Caterina Ida Zeppieri

Mathematische Nachrichten, 2025, vol. 298, issue 1, 312-327

Abstract: 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.

Date: 2025
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https://doi.org/10.1002/mana.202300346

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