The non-convex planar least gradient problem

IF 1.3 2区数学 Q1 MATHEMATICS

Nonlinear Analysis-Theory Methods & Applications Pub Date : 2025-05-22 DOI:10.1016/j.na.2025.113843

Samer Dweik , Piotr Rybka , Ahmad Sabra

引用次数: 0

Abstract

We study the least gradient problem in bounded regions with Lipschitz boundary in the plane. We provide a set of conditions for the existence of solutions in non-convex simply connected regions. We assume the boundary data is continuous and in the space of functions of bounded variation, and we are interested in solutions that satisfy the boundary conditions in the trace sense. Our method relies on the equivalence of the least gradient problem and the Beckmann problem which allows us to use the tools of the optimal transportation theory.

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非凸平面最小梯度问题

研究了平面上具有Lipschitz边界的有界区域上的最小梯度问题。给出了非凸单连通区域解存在的一组条件。我们假设边界数据是连续的，并且在有界变分函数的空间中，我们感兴趣的是在迹意义上满足边界条件的解。我们的方法依赖于最小梯度问题和贝克曼问题的等价性，这使我们能够使用最优运输理论的工具。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Nonlinear Analysis-Theory Methods & Applications 数学-数学

CiteScore

3.30

自引率

0.00%

发文量

265

审稿时长

60 days

期刊介绍： Nonlinear Analysis focuses on papers that address significant problems in Nonlinear Analysis that have a sustainable and important impact on the development of new directions in the theory as well as potential applications. Review articles on important topics in Nonlinear Analysis are welcome as well. In particular, only papers within the areas of specialization of the Editorial Board Members will be considered. Authors are encouraged to check the areas of expertise of the Editorial Board in order to decide whether or not their papers are appropriate for this journal. The journal aims to apply very high standards in accepting papers for publication.