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We investigate unique continuation properties and asymptotic behaviour atboundary points for solutions to a class of elliptic equations involving thespectral fractional Laplacian. An extension procedure leads us to study adegenerate or singular equation on a cylinder, with a homogeneous Dirichletboundary condition on the lateral surface and a non homogeneous Neumanncondition on the basis. For the extended problem, by an Almgren-typemonotonicity formula and a blow-up analysis, we classify the local asymptoticprofiles at the edge where the transition between boundary conditions occurs.Passing to traces, an analogous blow-up result and its consequent strong uniquecontinuation property is deduced for the nonlocal fractional equation.

Strong unique continuation from the boundary for the spectral fractional Laplacian