Revista Matemática Iberoamericana
Full-Text PDF (466 KB) | Metadata | Table of Contents | RMI summary
Published online: 2018-12-17
Isolated singularities for a semilinear equation for the fractional Laplacian arising in conformal geometryAzahara DelaTorre and María del Mar González (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