Approximation of $SBV$ functions with possibly infinite jump set

Sergio Conti, Matteo Focardi, Flaviana Iurlano

We prove an approximation result for functions $u\in SBV(\Omega ;{\mathbb{R}}^m)$ such that $\nabla u$ is $p$-integrable, $1\le p<\infty$, and $g_0(|[u]|)$ is integrable over the jump set…