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arXiv · 1703.07297

Separable infinite harmonic functions in cones

Marie-Françoise Bidaut-Véron·Marta Garcia-Huidobro·Laurent Véron
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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, $\sigma$) = r --$\beta$ $\omega$($\sigma$). We prove that such solutions exist, the spherical part $\omega$ satisfies a nonlinear eigenvalue problem on a subdomain of the sphere S N --1 and that the exponents $\beta$ = $\beta$ + > 0 and $\beta$ = $\beta$ -- < 0 are uniquely determined if the domain is smooth.

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Marie-Françoise Bidaut-Véron, Marta Garcia-Huidobro, Laurent Véron. 2017-03-21. Separable infinite harmonic functions in cones. https://arxiv.org/abs/1703.07297

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