Lower semicontinuity of nonlocal $L^\infty $ energies on $SBV_0(I)$

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 $[u](r):=u(r^+)- u(r^-)$,...

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Bibliographic Details

Published in:	Comptes Rendus. Mathématique
Main Authors:	Matias, José, Santos, Pedro Miguel, Zappale, Elvira
Format:	Article
Language:	English
Published:	Académie des sciences 2025-05-01
Subjects:	Cartesian submaximality nonlocal $L^\infty $ energies interfacial energy lower semicontinuity nonlocal gradients supremal functionals
Online Access:	https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.726/