Analysis of Bounded Variation Function Space and Critical Points in 1-Laplacian Operator Problems: A Systematic Review

Abstract

This paper presents a systematic review on the space of bounded variation functions and critical points in problems related to the 1-Laplacian operator. Bounded variation is a fundamental concept in functional analysis and theory of differential equations, relevant to understanding the behavior of solutions in various variational problems. The 1-Laplacian operator, which arises in contexts such as image theory and shape analysis, poses unique challenges due to its nonlinearity and the singular properties of its solutions. That is why this research focuses on the role those various nations, researchers and institutions play in underlining international collaboration, establishing connections and partnerships with research centers around the world, which allows access to up-to-date knowledge on the subject, such as the exchange of ideas and the development of international scientific capabilities. This systematic review allows for a compact examination of the current state of the art in the analysis of bounded variation function space and critical points in problems related to the 1-Laplacian operator, through the analysis of 129 articles collected from the SCOPUS database and 125 from WoS, highlighting the leadership of countries such as China, Italy, and France, as major players, emphasizing their significant contributions to the advancement and research in this field. The study shows that international collaboration has been fundamental for scientists and institutions to build strategic alliances and global research centers. Major challenges have been identified, such as investment in talent training and development in this field due to the limited data found.