Lower semicontinuity of nonlocal $L^∞ $ energies on $SBV_0(I)$ - Matias, José; Santos, Pedro Miguel; Zappale, Elvira (Comptes Rendus. Mathématique, 2025)
We characterize the lower-semicontinuity of nonlocal one-dimensional energies of the type \[ \operatorname{ess\;sup}_{(s,t) \in I\times I} h\bigl ([u](s), [u](t)\bigr ), \] where $I$ is an open and bounded interval in the real line, $u \in \mathit{SBV_{\mathrm{0}}}(I)$ and $[u](r):=u(r^+)- u(r^-)$, with $r\in I$.