Rigidity of balls in the solid mean value property for polyharmonic functions
Analysis of PDEs
2026-03-11 v1
Abstract
We show that balls are the only open bounded domains for which the mean value formula for polyharmonic functions holds. We do so by adapting an argument of \"U. Kuran for harmonic functions. Also, we provide a quantitative version of the same result.
Keywords
Cite
@article{arxiv.2603.09409,
title = {Rigidity of balls in the solid mean value property for polyharmonic functions},
author = {Nicola Abatangelo},
journal= {arXiv preprint arXiv:2603.09409},
year = {2026}
}