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

Abstract

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.

41 pages, 2 figures

References in corpus (1)

• On higher order extensions for the fractional Laplacian

Cited by in corpus (2)

• Unique continuation from conical boundary points for fractional equations
• On the fractional powers of a Schrödinger operator with a Hardy-type potential