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

## TL;DR

This paper establishes the existence and uniqueness of p-harmonic functions with specific asymptotic behavior in conical domains generated by non-smooth spherical surfaces, extending understanding of such functions in irregular geometries.

## Contribution

It proves the existence and uniqueness of p-harmonic functions of a specific form in non-smooth conical domains, generalizing previous results to irregular spherical boundaries.

## Key findings

- Existence of p-harmonic functions in non-smooth cones.
- Uniqueness of the exponent and normalized function under Lipschitz conditions.
- Extension of classical results to irregular spherical 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.