In the development of potential theory we mostly study harmonic functions. However I found some paper, which present potential theory as the study of potentials.
Are potentials harmonic functions?
2026-03-29 04:34:16.1774758856
Potential theory, potentials and harmonic functions
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Potentials may be harmonic in some places. For example, the potential of a point mass/charge is harmonic everywhere except at one point. In physical terms, the potential is harmonic in the regions that are free of masses/charges whose gravitational/electrostatic potential we consider.
At the beginning. Later on, subharmonic functions are dealt with most of the time. A key result connecting these notions is the Riesz decomposition theorem: a subharmonic function is the sum of a harmonic function and the potential of some measure.