On the properties of the set where a generalized function of bounded variation takes infinite value

2024/02/20 by Alessandro Cucinotta, Cucinotta, Alessandro
Computer Science · #Analysis of PDEs (math.AP) #FOS: Mathematics #Optimization and Variational Analysis

paper · pdf · doi:10.48550/arxiv.2402.13078

openalex publication_date 2024/02/20 · openalex created_date 2024/02/22 · openalex updated_date 2026/07/28

Abstract

We study the properties of the set where a generalized function of bounded variation has infinite approximate limit, highlighting in this way the main geometric difference with functions of bounded variation. To this aim we prove a new result on strict approximation of sets of finite perimeter from the outside with open sets.

Related

• Extensions and traces of functions of bounded variation on metric spaces
• Functions of bounded variation on complete and connected one-dimensional metric spaces
• Generalizing the Concept of Bounded Variation
• Existence and uniqueness of limits at infinity for bounded variation functions
• Quasiopen sets, bounded variation and lower semicontinuity in metric spaces