Given an open and bounded set Ω⊂RN, we consider the problem of minimizing the ratio between the s-perimeter and the N-dimensional Lebesgue measure among subsets of Ω. This is the nonlocal version of the well-known Cheeger problem. We prove various properties of optimal sets for this problem, as well as some equivalent formulations. In addition, the limiting behaviour of some nonlinear and nonlocal eigenvalue problems is investigated, in relation with this optimization problem. The presentation is as self-contained as possible.
Lorenzo Brasco
1
;
Erik Lindgren
2
;
Enea Parini
1
1
Aix-Marseille Université, France
2
KTH Royal Institute of Technology, Stockholm, Sweden
Lorenzo Brasco; Erik Lindgren; Enea Parini. The fractional Cheeger problem. Interfaces and free boundaries, Tome 16 (2014) no. 3, pp. 419-458. doi: 10.4171/ifb/325
@article{10_4171_ifb_325,
author = {Lorenzo Brasco and Erik Lindgren and Enea Parini},
title = {The fractional {Cheeger} problem},
journal = {Interfaces and free boundaries},
pages = {419--458},
year = {2014},
volume = {16},
number = {3},
doi = {10.4171/ifb/325},
url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/325/}
}
TY - JOUR
AU - Lorenzo Brasco
AU - Erik Lindgren
AU - Enea Parini
TI - The fractional Cheeger problem
JO - Interfaces and free boundaries
PY - 2014
SP - 419
EP - 458
VL - 16
IS - 3
UR - http://geodesic.mathdoc.fr/articles/10.4171/ifb/325/
DO - 10.4171/ifb/325
ID - 10_4171_ifb_325
ER -
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%A Erik Lindgren
%A Enea Parini
%T The fractional Cheeger problem
%J Interfaces and free boundaries
%D 2014
%P 419-458
%V 16
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4171/ifb/325/
%R 10.4171/ifb/325
%F 10_4171_ifb_325
