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
Fall, M., Felli, V. (2014). Unique Continuation Property and Local Asymptotics of Solutions to Fractional Elliptic Equations. COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 39(2), 354-397 [10.1080/03605302.2013.825918].
Unique Continuation Property and Local Asymptotics of Solutions to Fractional Elliptic Equations
FALL, MOUHAMED MOUSTAPHA;FELLI, VERONICA
2014
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
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