Regularity of sets of finite fractional perimeter and nonlocal minimal surfaces in metric measure spaces

2024/01/10 by Josh Kline, Kline, Josh
Mathematics · #Fixed Point Theorems Analysis #Analytic and geometric function theory #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2401.04891

Abstract

In the setting of a doubling metric measure space, we study regularity of sets with finite s-perimeter, that is, sets whose characteristic functions have finite Besov energy, with regularity parameter 0

Related

• Fractional Perimeter and Nonlocal Minimal Surfaces
• Periodic partitions with minimal perimeter
• A Federer-style characterization of sets of finite perimeter on metric spaces
• Approximation of sets of finite fractional perimeter by smooth sets and comparison of local and global s-minimal surfaces
• Nonlocal minimal surfaces: interior regularity, quantitative estimates and boundary stickiness