Non-degeneracy of the bubble in a fractional and singular 1D Liouville equation

2024/04/22 by DelaTorre, Azahara, Mancini, Gabriele, Pistoia, Angela +1 · 1 citation
#35A02) #35R11 (35B33 #45G05 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2404.14119

Abstract

We prove the non-degeneracy of solutions to a fractional and singular Liouville equation defined on the whole real line in presence of a singular term. We use conformal transformations to rewrite the linearized equation as a Steklov eigenvalue problem posed in a bounded domain, which is defined either by an intersection or a union of two disks. We conclude by proving the simplicity of the corresponding eigenvalue.

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