Existence and comparison results for an elliptic equation involving the 1-Laplacian and L¹-data

2016/07/22 by Marta Latorre, Latorre, M., Sergio Segura de León +1 · 2 citations
Computer Science · Mathematics · #35J15 #35J25 #35J60 #35J75 #Advanced Mathematical Modeling in Engineering #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1607.06653

openalex publication_date 2016/07/22 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

Abstract

This paper is devoted to analyse the Dirichlet problem for a nonlinear elliptic equation involving the 1--Laplacian and a total variation term, that is, the inhomogeneous case of the equation arising in the level set formulation of the inverse mean curvature flow. We study this problem in an open bounded set with Lipschitz boundary. We prove an existence result and a comparison principle for non--negative L¹--data. Moreover, we search the summability that the solution reaches when more regular L^p--data, with 1

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