Separable p-harmonic functions in a cone and related quasilinear equations on manifolds

TL;DR

This paper provides a new proof for the existence of separable p-harmonic functions in a cone within Riemannian manifolds with nonnegative Ricci curvature, extending understanding of quasilinear elliptic equations.

Contribution

It offers a novel proof of Tolksdorf's result on separable p-harmonic functions, applicable to manifolds with nonnegative Ricci curvature.

Findings

Existence of separable p-harmonic functions in cones

Extension of Tolksdorf's result to Riemannian manifolds

New proof technique for quasilinear elliptic equations

Abstract

In considering a class of quasilinear elliptic equations on a Riemannian manifold with nonnegative Ricci curvature, we give a new proof of Tolksdorf's result on the construction of separable $p$-harmonic functions in a cone.