Three spheres theorem for p-harmonic functions

TL;DR

This paper establishes a three spheres theorem for p-harmonic functions in Euclidean space, extending classical results to nonlinear potential theory and providing new insights into their behavior.

Contribution

It introduces a three spheres theorem specifically for p-harmonic functions on the complement of k-balls, a novel extension in nonlinear analysis.

Findings

Proves a three spheres inequality for p-harmonic functions

Extends classical three spheres results to nonlinear p-harmonic case

Provides tools for analyzing p-harmonic functions in complex geometries

Abstract

Three spheres type theorem is proved for the p-harmonic functions defined on the complement of k-balls in the Euclidean n-dimensional space.