Submitted Paper
Inserted: 5 feb 2018
Last Updated: 10 nov 2018
Pages: 22
Year: 2018
Abstract:
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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