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

Mouhamed Moustapha Fall; Veronica Felli

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arXiv · 1301.5119

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

Mouhamed Moustapha Fall·Veronica Felli

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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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Mouhamed Moustapha Fall, Veronica Felli. 2013-07-14. Unique continuation property and local asymptotics of solutions to fractional elliptic equations. https://arxiv.org/abs/1301.5119

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