We prove the non-degeneracy of solutions to a fractional and singular Liouville equation defined on the whole real line in the 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.
Non-degeneracy of the bubble in a fractional and singular 1D Liouville equation
Mancini, Gabriele;
2026-01-01
Abstract
We prove the non-degeneracy of solutions to a fractional and singular Liouville equation defined on the whole real line in the 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.File in questo prodotto:
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