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arXiv · 2404.14119

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

Azahara DelaTorre·Gabriele Mancini·Angela Pistoia·Luigi Provenzano
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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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Azahara DelaTorre, Gabriele Mancini, Angela Pistoia, Luigi Provenzano. 2024-04-22. Non-degeneracy of the bubble in a fractional and singular 1D Liouville equation. https://arxiv.org/abs/2404.14119

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