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

Alessandra De Luca, Veronica Felli, Stefano Vita

Published 2021-03-08Version 1

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