WIAS Preprint No. 2256, (2016)

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


  • Dipierro, Serena
  • Soave, Nicola
  • Valdinoci, Enrico
    ORCID: 0000-0001-6222-2272

2010 Mathematics Subject Classification

  • 35R11 26A33 60G22 35J91


  • nonlocal semilinear equations, sliding methods, monotonicity, regularity, symmetry




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 [4].

Appeared in

  • Math. Anal., 369:3-4 (2017) pp. 1283--1326.

Download Documents