JournalsaihpcVol. 38, No. 5pp. 1407–1428

On critical points of the relative fractional perimeter

  • Dayana Pagliardini

    Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126 Pisa, Italy

  • Andrea Malchiodi

    Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126 Pisa, Italy

  • Matteo Novaga

    Dipartimento di Matematica, Università di Pisa, Largo B. Pontecorvo 5, 56217 Pisa, Italy
On critical points of the relative fractional perimeter cover

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Abstract

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. 1407–1428

DOI 10.1016/J.ANIHPC.2020.11.005