On characterization of balls via solutions to the Helmholtz equation

2022/03/28 by Н. В. Кузнецов, Kuznetsov, Nikolay
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Composite Material Mechanics #FOS: Mathematics #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2203.14833

openalex publication_date 2022/03/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A new analytical characterization of balls in the Euclidean space \RR^m is obtained. Unlike previous results of this kind, using either harmonic functions or solutions to the modified Helmholtz equation, the present one is based on solutions to the Helmholtz equation. This is achieved at the expense of a restriction imposed on the size of a domain -- a feature absent in the inverse mean value properties known before.

Related

• Inverse mean value property of solutions to the modified Helmholtz equation
• A characterisation of harmonic functions by quadrature identities of annular domains and related results
• Characterizations of discs via weighted means
• On the three ball theorem for solutions of the Helmholtz equation
• Characterization of harmonic and subharmonic functions via mean-value properties