  This note is a synthesis of my reflexions on some questions that have emerged
during the MATRIX event "Recent Trends on Nonlinear PDEs of Elliptic and
Parabolic Type" concerning the qualitative properties of solutions to some non
local reaction-diffusion equations of the form L[u](x) + f (u(x)) = 0, for x
$\in$ R n \ K, where K $\subset$ R N is a bounded smooth compact "obstacle", L
is non local operator and f is a bistable nonlinearity. When K is convex and
the nonlocal operator L is a continuous operator of convolution type then some
Liouville-type results for solutions satisfying some asymptotic limiting
conditions at infinity have been recently established by Brasseur, Coville,
Hamel and Valdinoci [4]. Here, we show that for a bounded smooth convex
obstacle K, similar Liouville type results hold true when the operator L is the
regional s-fractional Laplacian.
