Unique Continuation from Conical Boundary Points for Fractional Equations

We provide fine asymptotics of solutions of fractional elliptic equations at boundary points where the domain is locally conical; that is, corner type singularities appear. Our method relies on a suitable smoothing of the corner singularity and an approximation scheme, which allow us to provide a Pohozaev- type inequality. Then the asymptotics of solutions at the conical point follow by an Almgren-type monotonicity formula, blow-up analysis, and Fourier decomposition on eigenspaces of a spherical eigenvalue problem. A strong unique continuation principle follows as a corollary.