Mean value properties of solutions to the modified Helmholtz equation and related topics (a survey)
Nikolay Kuznetsov
TL;DR
This survey reviews recent advances in mean value properties of solutions to the modified Helmholtz equation, exploring their connections to harmonic functions, inverse properties, and related mathematical topics.
Contribution
It compiles and discusses recent results on mean value properties and their implications for solutions of the modified Helmholtz equation.
Findings
Mean value properties characterize solutions to the modified Helmholtz equation.
Inverse and converse properties link these solutions to harmonic functions.
The survey highlights relations between modified Helmholtz solutions and harmonic analysis.
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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Taxonomy
TopicsNumerical methods in inverse problems · Acoustic Wave Phenomena Research · Electromagnetic Scattering and Analysis