We study the localization of sets with constant nonlocal mean curvature and prescribed small volume in a bounded open set, proving that they are sufficiently close to critical points of a suitable nonlocal potential. We then consider the fractional perimeter in half-spaces. We prove existence of minimizers under fixed volume constraint, and we show some properties such as smoothness and rotational symmetry.
Cite this article
Dayana Pagliardini, Andrea Malchiodi, Matteo Novaga, On critical points of the relative fractional perimeter. Ann. Inst. H. Poincaré Anal. Non Linéaire 38 (2021), no. 5, pp. 1407–1428DOI 10.1016/J.ANIHPC.2020.11.005