Unique continuation property and local asymptotics of solutions to fractional elliptic equations. (English) Zbl 1286.35250
Summary: Asymptotics of solutions to fractional elliptic equations with Hardy type potentials are 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.
MSC:
| 35R11 | Fractional partial differential equations |
| 35B40 | Asymptotic behavior of solutions to PDEs |
| 35J60 | Nonlinear elliptic equations |
| 35J75 | Singular elliptic equations |
Keywords:
Caffarelli-Silvestre extension; fractional elliptic equations; Hardy inequality; unique continuation propertyReferences:
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