Delaunay-type singular solutions for the fractional Yamabe Problem

2015/10/28 by Azahara DelaTorre, DelaTorre, A., Manuel del Pino +5 · 1 citation
Computer Science · Mathematics · #35B33 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1510.08504

openalex publication_date 2015/10/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct Delaunay-type solutions for the fractional Yamabe problem with an isolated singularity (-Δ)^γw = c_{n, γ} w^{(n+2γ)/(n-2γ)}, w>0 in ℝⁿ \backslash \0\ We follow a variational approach, in which the key is the computation of the fractional Laplacian in polar coordinates.

Citations

• Regularity of the obstacle problem for a fractional power of the laplace operator
• A direct method of moving spheres on fractional order equations

Cited by

• Classification of fractional, singular Yamabe metrics on a twice punctured sphere I

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