Lower semicontinuity of nonlocal $L^\infty$ energies on $SBV_0(I)$
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866910879818186752 |
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| author | Matias, Jose Santos, Pedro M. Zappale, Elvira |
| author_facet | Matias, Jose Santos, Pedro M. Zappale, Elvira |
| contents | We characterize the lower-semicontinuity of nonlocal one-dimensional energies of the type \[{\rm ess}\!\!\!\!\!\!\!\!\sup_{(s,t) \in I\times I} h([u](s), [u](t)),\] where $I$ is an open and bounded interval in the real line, $u \in SBV_0(I)$ and $[u](r):= u(r^+)- u(r^-)$, with $r\in I$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_02218 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Lower semicontinuity of nonlocal $L^\infty$ energies on $SBV_0(I)$ Matias, Jose Santos, Pedro M. Zappale, Elvira Analysis of PDEs 49J45, 26B25, 26A45, 26A51 We characterize the lower-semicontinuity of nonlocal one-dimensional energies of the type \[{\rm ess}\!\!\!\!\!\!\!\!\sup_{(s,t) \in I\times I} h([u](s), [u](t)),\] where $I$ is an open and bounded interval in the real line, $u \in SBV_0(I)$ and $[u](r):= u(r^+)- u(r^-)$, with $r\in I$. |
| title | Lower semicontinuity of nonlocal $L^\infty$ energies on $SBV_0(I)$ |
| topic | Analysis of PDEs 49J45, 26B25, 26A45, 26A51 |
| url | https://arxiv.org/abs/2501.02218 |