Calculus of Variations and Geometric Measure Theory

S. Dipierro - N. Soave - E. Valdinoci

On fractional elliptic equations in Lipschitz sets and epigraphs: regularity, monotonicity and rigidity results.

created by soave on 07 Dec 2016


Accepted Paper

Inserted: 7 dec 2016
Last Updated: 7 dec 2016

Journal: Mathematische Annalen
Year: 2016
Doi: 10.1007/s00208-016-1487-x
Links: Link


We consider a nonlocal equation set in an unbounded domain with the epigraph property. We prove symmetry, monotonicity and rigidity results. In particular, we deal with halfspaces, coercive epigraphs and epigraphs that are flat at infinity. These results can be seen as the nonlocal counterpart of the celebrated article (Berestycki et al., Commun Pure Appl Math 50(11):1089–1111, 1997).