On Relations between Harmonic and Panharmonic Functions

The m-dimensional modified Helmholtz equation is considered and two relations between its solutions (called panharmonic functions) and harmonic functions are established in a bounded domain. Both relations essentially rely on properties of the Newtonian potential. Other characteristics of panharmoni...

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Bibliographic Details
Published in:Journal of mathematical sciences (New York, N.Y.) N.Y.), 2022-11, Vol.267 (4), p.494-500
Main Author: Kuznetsov, N.
Format: Article
Language:English
Subjects:
Harmonic functions
Helmholtz equations
Mathematics
Mathematics and Statistics
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Summary:The m-dimensional modified Helmholtz equation is considered and two relations between its solutions (called panharmonic functions) and harmonic functions are established in a bounded domain. Both relations essentially rely on properties of the Newtonian potential. Other characteristics of panharmonic functions are also obtained.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-022-06154-7