Evolution problem for the $1$-Laplacian with mixed boundary conditions

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Autori principali:	Igbida, N., Mazón, J. M., Toledo, J.
Natura:	Preprint
Pubblicazione:	2025
Soggetti:	Analysis of PDEs
Accesso online:	Acceder al recurso
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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

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