Separable infinite harmonic functions in cones

Abstract : We study the existence of separable infinite harmonic functions in any cone of R N vanishing on its boundary under the form u(r, σ) = r −β ω(σ). We prove that such solutions exist, the spherical part ω satisfies a nonlinear eigenvalue problem on a subdomain of the sphere S N −1 and that the exponents β = β + > 0 and β = β − < 0 are uniquely determined if the domain is smooth.
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  • HAL Id : hal-01492362, version 3
  • ARXIV : 1703.07297

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Marie-Françoise Bidaut-Véron, Marta Garcia-Huidobro, Laurent Véron. Separable infinite harmonic functions in cones. Calculus of Variations and Partial Differential Equations, In press, 35, pp.35 - 62. ⟨hal-01492362v3⟩

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