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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2508.01809 |
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| _version_ | 1866912517180096512 |
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| author | Igbida, N. Mazón, J. M. Toledo, J. |
| author_facet | Igbida, N. Mazón, J. M. Toledo, J. |
| contents | This paper deals with evolution problem for the $1$-Laplacian with mixed boundary conditions on a bounded open set $Ω$ of $\R^N$. We prove existence and uniqueness of strong solutions for data in $L^2(Ω)$ by mean of the theory of maximal monotone operator. We also see that if the flux on the boundary is~$1$ (that is, the maximum possible) then these strong solutions can be seen as the large solutions introduced in \cite{MP}. We give explicit examples of solutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_01809 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Evolution problem for the $1$-Laplacian with mixed boundary conditions Igbida, N. Mazón, J. M. Toledo, J. Analysis of PDEs This paper deals with evolution problem for the $1$-Laplacian with mixed boundary conditions on a bounded open set $Ω$ of $\R^N$. We prove existence and uniqueness of strong solutions for data in $L^2(Ω)$ by mean of the theory of maximal monotone operator. We also see that if the flux on the boundary is~$1$ (that is, the maximum possible) then these strong solutions can be seen as the large solutions introduced in \cite{MP}. We give explicit examples of solutions. |
| title | Evolution problem for the $1$-Laplacian with mixed boundary conditions |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2508.01809 |