Applications of the s-harmonic extension to the study of singularities of Emden’s equations

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Abstract

We use the Caffarelli–Silvestre extension to \( \mathrm{R}_+\times\mathrm{R}^N \) to study the isolated singularities of functions satisfying the semilinear fractional equation \( (-\Delta)^sv+\epsilon v^p=0 \) in a punctured domain of \( \mathrm{R}^N \) where \(\epsilon=\pm 1\), \(0 and \(p>1\). We emphasise the obtention of a priori estimates and analyse the set of self-similar solutions. We provide a complete description of the possible behaviour of solutions near a singularity.

About the authors

Laurent Veron

Université de Tours

Author for correspondence.
Email: veronl@univ-tours.fr
Тур, Франция

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