Calculus of Variations and Geometric Measure Theory
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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 13 Oct 2020


Accepted Paper

Inserted: 5 feb 2018
Last Updated: 13 oct 2020

Journal: Annales IHP - Analyse Nonlineaire
Pages: 22
Year: 2018

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 $\{x_N = 0\}$.


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