Strong unique continuation and local asymptotics at the boundary for fractional elliptic equations

We study local asymptotics of solutions to fractional elliptic equations at boundary points, under some outer homogeneous Dirichlet condition. Our analysis is based on a blow-up procedure which involves Almgren type monotonicity formulae and provides classification all possible homogeneity degrees limiting entire profiles. As consequence, we establish strong unique continuation principle from points.