Unique continuation property and local asymptotics of solutions to fractional elliptic equations

Abstract

Asymptotics of solutions to fractional elliptic equations with Hardy type potentials is studied in this paper. By using an Almgren type monotonicity formula, separation of variables, and blow-up arguments, we describe the exact behavior near the singularity of solutions to linear and semilinear fractional elliptic equations with a homogeneous singular potential related to the fractional Hardy inequality. As a consequence we obtain unique continuation properties for fractional elliptic equations.

This is a revision of arXiv:1301.5119v1: some minor changes have been made and Theorem 1.3 has been added

References in corpus (1)

• On a fractional Nirenberg problem, part I: blow up analysis and compactness of solutions

Cited by in corpus (2)

• Unique Continuation for Fractional Schrödinger Equations with Rough Potential
• On higher order extensions for the fractional Laplacian