A nonlocal approximation of the area in codimension two

2024/06/19 by Michele Caselli, Caselli, Michele, Mattia Freguglia +3 · 2 citations
Mathematics · #28A75 #49J45 #49Q20 #Analysis of PDEs (math.AP) #Approximation Theory and Sequence Spaces #Differential Equations and Boundary Problems #Differential Geometry (math.DG) #FOS: Mathematics #Mathematical functions and polynomials #Optimization and Control (math.OC)

paper · pdf · doi:10.48550/arxiv.2406.13696

openalex publication_date 2024/06/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For s∈ (0,1) we introduce a notion of fractional s-mass on (n-2)-dimensional closed, orientable surfaces in \Rⁿ. Moreover, we prove its Γ-convergence, with respect to the flat topology, and pointwise convergence to the (n-2)-dimensional area.

Cited by

• Γ-convergence for higher order nonlocal phase transitions
• Γ-convergence of the p-Dirichlet energy for manifold-valued maps

Related

• Fractional Perimeter and Nonlocal Minimal Surfaces
• Nonlocal s-minimal surfaces and Lawson cones
• Weyl Law and convergence in the classical limit for min-max nonlocal minimal surfaces
• On critical points of the relative fractional perimeter
• Quantitative flatness results and BV-estimates for stable nonlocal\n minimal surfaces