The spherical p-harmonic eigenvalue problem in non-smooth domains

Abstract

We prove the existence of p-harmonic functions under the form u(r, sigma) = r(-beta)omega(sigma) in any cone C-S generated by a spherical domain S and vanishing on partial derivative C-S. We prove the uniqueness of the exponent beta and of the normalized function omega under a Lipschitz condition on S. (C) 2017 Published by Elsevier Inc.