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.
Isolated singularities for a semilinear equation for the fractional Laplacian arising in conformal geometry / Delatorre, A.; Gonzalez, M. D. M.. - In: REVISTA MATEMATICA IBEROAMERICANA. - ISSN 0213-2230. - 34:4(2018), pp. 1645-1678. [10.4171/rmi/1038]
Isolated singularities for a semilinear equation for the fractional Laplacian arising in conformal geometry
DelaTorre A.;
2018
Abstract
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.File | Dimensione | Formato | |
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