Geodesic
On critical points of the relative fractional perimeter
Malchiodi, Andrea1 ; Novaga, Matteo2 ; Pagliardini, Dayana1
1 a Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126 Pisa, Italy
2 b Dipartimento di Matematica, Università di Pisa, Largo B. Pontecorvo 5, 56217 Pisa, Italy
Annales de l'I.H.P. Analyse non linéaire, septembre – octobre 2021, Tome 38 (2021) no. 5, pp. 1407-1428

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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.

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DOI : 10.1016/j.anihpc.2020.11.005
Keywords: Fractional mean curvature, Isoperimetric sets, Perturbative variational theory

Malchiodi, Andrea 1 ; Novaga, Matteo 2 ; Pagliardini, Dayana 1

1 a Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126 Pisa, Italy
2 b Dipartimento di Matematica, Università di Pisa, Largo B. Pontecorvo 5, 56217 Pisa, Italy 
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     title = {On critical points of the relative fractional perimeter},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {1407--1428},
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Malchiodi, Andrea; Novaga, Matteo; Pagliardini, Dayana. On critical points of the relative fractional perimeter. Annales de l'I.H.P. Analyse non linéaire, septembre – octobre 2021, Tome 38 (2021) no. 5, pp. 1407-1428. doi: 10.1016/j.anihpc.2020.11.005

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