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 $r\in I$.
Nous caractérisons la semi-continuité inférieure des énergies non locales unidimensionnelles
\[ \operatorname{ess\;sup}_{(s,t) \in I\times I} h\bigl ([u](s), [u](t)\bigr ), \] |
où I est un intervalle ouvert et borné dans l’axe réel, $u \in \mathit{SBV_{\mathrm{0}}}(I)$ et $[u](r):=u(r^+)- u(r^-)$ avec $r\in I$.
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Keywords: Cartesian submaximality, nonlocal $L^\infty $ energies, interfacial energy, lower semicontinuity, nonlocal gradients, supremal functionals
Mots-clés : Sous-maximalité cartésienne, énergies $L^\infty $ non locales, énergie interfaciale, semi-continuité inférieure, gradients non locaux, fonctionnelles suprémales
José Matias 1; Pedro Miguel Santos 1; Elvira Zappale 2, 3

@article{CRMATH_2025__363_G4_407_0, author = {Jos\'e Matias and Pedro Miguel Santos and Elvira Zappale}, title = {Lower semicontinuity of nonlocal $L^\infty $ energies on $SBV_0(I)$}, journal = {Comptes Rendus. Math\'ematique}, pages = {407--414}, publisher = {Acad\'emie des sciences, Paris}, volume = {363}, year = {2025}, doi = {10.5802/crmath.726}, language = {en}, }
TY - JOUR AU - José Matias AU - Pedro Miguel Santos AU - Elvira Zappale TI - Lower semicontinuity of nonlocal $L^\infty $ energies on $SBV_0(I)$ JO - Comptes Rendus. Mathématique PY - 2025 SP - 407 EP - 414 VL - 363 PB - Académie des sciences, Paris DO - 10.5802/crmath.726 LA - en ID - CRMATH_2025__363_G4_407_0 ER -
José Matias; Pedro Miguel Santos; Elvira Zappale. Lower semicontinuity of nonlocal $L^\infty $ energies on $SBV_0(I)$. Comptes Rendus. Mathématique, Volume 363 (2025), pp. 407-414. doi : 10.5802/crmath.726. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.726/
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