Revista Matemática Iberoamericana


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Volume 34, Issue 4, 2018, pp. 1645–1678
DOI: 10.4171/rmi/1038

Published online: 2018-12-17

Isolated singularities for a semilinear equation for the fractional Laplacian arising in conformal geometry

Azahara DelaTorre[1] and María del Mar González[2]

(1) Universität Freiburg, Germany
(2) Universidad Autónoma de Madrid, Spain

We consider radial solutions with an isolated singularity for a semilinear equation involving the fractional Laplacian. In conformal geometry, this is equivalent to the study of singular metrics with constant fractional curvature (singular fractional Yamabe problem). Our main ideas are: first, to set up the problem into a natural geometric framework; and second, to reduce the problem to a non-local ODE for which we are able to perform some kind of phase portrait study.

Keywords: Isolated singularities, fractional Laplacian, cylinder, radial solutions, fractional Yamabe problem, non-local ODE

DelaTorre Azahara, González María del Mar: Isolated singularities for a semilinear equation for the fractional Laplacian arising in conformal geometry. Rev. Mat. Iberoam. 34 (2018), 1645-1678. doi: 10.4171/rmi/1038