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Mean value properties of solutions to the modified Helmholtz equation and related topics (a survey)

2022/08/26 by Н. В. Кузнецов, Nikolay Kuznetsov, Kuznetsov, Nikolay
Engineering · Mathematics · Physics and Astronomy · #Acoustic Wave Phenomena Research #Analysis of PDEs (math.AP) #Electromagnetic Scattering and Analysis #FOS: Mathematics #Numerical methods in inverse problems #math.AP

paper · pdf · doi:10.48550/arxiv.2208.12840

24 pages, no figures. arXiv admin note: text overlap with arXiv:2207.11729

arxiv created 2022/08/26 · openalex publication_date 2022/08/26 · arxiv updated 2022/08/30 · openalex created_date 2022/08/31 · openalex updated_date 2026/07/28

Abstract

Recent results concerning solutions of the modified Helmholtz equation are reviewed; namely, various mean value properties and their corollaries, converse and inverse of these properties, and relations between these solutions and harmonic functions.

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