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Journal Articles Journal of Differential Equations Year : 2023

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

Abstract

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.
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Dates and versions

hal-03689999 , version 1 (07-06-2022)
hal-03689999 , version 2 (03-03-2023)

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