Separable infinite harmonic functions in cones
Analysis of PDEs
2018-01-22 v3
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, ) = r -- (). We prove that such solutions exist, the spherical part satisfies a nonlinear eigenvalue problem on a subdomain of the sphere S N --1 and that the exponents = + > 0 and = -- < 0 are uniquely determined if the domain is smooth.
Cite
@article{arxiv.1703.07297,
title = {Separable infinite harmonic functions in cones},
author = {Marie-Françoise Bidaut-Véron and Marta Garcia-Huidobro and Laurent Véron},
journal= {arXiv preprint arXiv:1703.07297},
year = {2018}
}