Unique continuation from conical boundary points for fractional equations

Abstract

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.

33 pages, 3 figures

References in corpus (5)

• An extension problem related to the fractional Laplacian
• On a fractional Nirenberg problem, part I: blow up analysis and compactness of solutions
• Liouville type theorems and regularity of solutions to degenerate or singular problems part I: even solutions
• On s-harmonic functions on cones
• Strong unique continuation and local asymptotics at the boundary for fractional elliptic equations