Unique Continuation Property and Local Asymptotics of Solutions to Fractional Elliptic Equations |
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Authors: | Mouhamed Moustapha Fall |
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Institution: | African Institute for Mathematical Sciences (A.I.M.S.) of Senegal , Mbour , Sénégal |
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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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Keywords: | Caffarelli-Silvestre extension Fractional elliptic equations Hardy inequality Unique continuation property |
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