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arXiv · 2508.01809

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

N. Igbida·J. M. Mazón·J. Toledo
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Abstract

This paper deals with evolution problem for the $1$-Laplacian with mixed boundary conditions on a bounded open set $\Omega$ of $\R^N$. We prove existence and uniqueness of strong solutions for data in $L^2(\Omega)$ 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.

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N. Igbida, J. M. Mazón, J. Toledo. 2025-08-03. Evolution problem for the $1$-Laplacian with mixed boundary conditions. https://arxiv.org/abs/2508.01809

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