Preprint

Inserted: 1 jun 2023
Last Updated: 21 jul 2023

Year: 2023

Abstract:

In this note we show that $\mathrm{SBV}$ functions with jump normal lying in a prescribed set of directions $\mathcal N$ can be approximated by sequences of $\mathrm{SBV}$ functions whose jump set is essentially closed, polyhedral, and preserves the orthogonality to $\mathcal N$, moreover the functions are smooth away from their jump set. This approximation result is proven with respect to a strong convergence for which a large class of free-discontinuity functionals is continuous.

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