Singularities of fractional Emden's equations via Caffarelli-Silvestre extension

Huyuan Chen (1) , Laurent Véron (2)

1 Jiangxi Normal University
2 IDP - Institut Denis Poisson

We study the isolated singularities of functions satisfying (E) (−∆) s v±|v| p−1 v = 0 in Ω\{0}, v = 0 in R N \Ω, where 0 < s < 1, p > 1 and Ω is a bounded domain containing the origin. We use the Caffarelli-Silvestre extension to R + × R N. We emphasize the obtention of a priori estimates, analyse the set of self-similar solutions via energy methods to characterize the singularities.

Mots clés: Lane-Emden-Fowler equation; Linear extension; Energy methods; Limit set; AMS Subject Classification: 35B40-35J60-35J70-45G05 Fractional Laplacian; Isolated singularity

Domaines: Equations aux dérivées partielles [math.AP]

Huyuan Chen, Laurent Véron. Singularities of fractional Emden's equations via Caffarelli-Silvestre extension. Journal of Differential Equations, In press. ⟨hal-03689999v2⟩