On fractional elliptic equations in Lipschitz sets and epigraphs:   regularity, monotonicity and rigidity results
  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. 
Serena Dipierro, Nicola Soave and Enrico Valdinoci
math.AP