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 $\partial$C S. We prove the uniqueness of the exponent $\beta$ and of the normalized function $\omega$ under a Lipschitz condition on S.