Existence and uniqueness for the inhomogeneous 1-Laplace evolution equation revisited

Marta Latorre; Sergio Segura de León

Existence and uniqueness for the inhomogeneous 1-Laplace evolution equation revisited

Analysis of PDEs 2022-09-07 v2

Authors: Marta Latorre , Sergio Segura de León

Abstract

In this paper we deal with an inhomogeneous parabolic Dirichlet problem involving the 1-Laplacian operator. We show the existence of a unique solution when data belong to $L^1(0,T;L^2(\Omega))$ for every $T>0$ . As a consequence, global existence and uniqueness for data in $L^1_{loc}(0,+\infty;L^2(\Omega))$ is obtained. Our analysis retrieves the results of \cite{SW} in a correct and complete way.

Keywords

1-laplacian parabolic dirichlet problem existence and uniqueness inhomogeneous equation global solution

Cite

@article{arxiv.2203.12571,
  title  = {Existence and uniqueness for the inhomogeneous 1-Laplace evolution equation revisited},
  author = {Marta Latorre and Sergio Segura de León},
  journal= {arXiv preprint arXiv:2203.12571},
  year   = {2022}
}

Comments

32 pages

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