Calculus of Variations and Geometric Measure Theory

G. E. Comi - G. Stefani

On sets with finite distributional fractional perimeter

created by stefani on 19 Mar 2023
modified on 21 Mar 2023


Submitted Paper

Inserted: 19 mar 2023
Last Updated: 21 mar 2023

Year: 2023

ArXiv: 2303.10989 PDF


We continue the study of the fine properties of sets having locally finite distributional fractional perimeter. We refine the characterization of their blow-ups and prove a Leibniz rule for the intersection of sets with locally finite distributional fractional perimeter with sets with finite fractional perimeter. As a byproduct, we provide a description of non-local boundaries associated with the distributional fractional perimeter.

Keywords: Fractional Gradient, fractional perimeter, Leibniz rule, Blow-up Theorem, non-local boundary