Calculus of Variations and Geometric Measure Theory

G. Lazzaroni - P. Wozniak - C. I. Zeppieri

Strong approximation of SBV functions with prescribed jump direction

created by zeppieri1 on 01 Jun 2023
modified on 21 Jul 2023



Inserted: 1 jun 2023
Last Updated: 21 jul 2023

Year: 2023


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.