Unique Continuation Property and Local Asymptotics of Solutions to Fractional Elliptic Equations

作者：Fall, Mouhamed Moustapha; Felli, Veronica^*

来源：Communications in Partial Differential Equations, 2014, 39(2): 354-397.

DOI：10.1080/03605302.2013.825918

• Caffarelli-Silvestre extension
• Fractional elliptic equations
• Hardy inequality
• Unique continuation property
• 35R11
• 35B40
• 35J60
• 35J75

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.

• 出版日期2014-2-1