Calculus of Variations and Geometric Measure Theory

A. Malchiodi - M. Novaga - D. Pagliardini

On critical points of the relative fractional perimeter

created by pagliardini on 05 Feb 2018
modified by novaga on 19 Aug 2021


Published Paper

Inserted: 5 feb 2018
Last Updated: 19 aug 2021

Journal: Annales IHP - Analyse Nonlineaire
Volume: 38
Number: 5
Pages: 1407–1428
Year: 2021

ArXiv: 1802.01510 PDF


Abstract. We study the localization of sets with constant nonlocal mean curvature and prescribed small volume in a bounded open set with smooth boundary, proving that they are sufficiently close to critical points of a suitable non-local potential. We then consider the fractional perimeter in half-spaces. We prove the existence of a minimizer under fixed volume constraint, showing some of its properties such as smoothness and symmetry, being a graph in the $x_N$-direction, and characterizing its intersection with the hyperplane $\{x_N = 0\}$.