Harmonic Functions

  • Oliver Dimon Kellogg
Part of the Die Grundlehren der Mathematischen Wissenschaften book series (GL, volume 31)


We have seen that Newtonian potentials are solutions of Laplace’s equation at points free from masses. We shall soon learn that solutions of Laplace’s equation are always Newtonian potentials, so that in studying the properties of such solutions, we are also studying the properties of Newtonian fields. We shall find that a surprising number of general properties follow from the mere fact that a function satisfies Laplace’s equation, or is harmonic, as we shall say.


Harmonic Function Interior Point Normal Derivative Divergence Theorem Closed Region 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1967

Authors and Affiliations

  • Oliver Dimon Kellogg
    • 1
  1. 1.Harvard UniversityCambridgeUSA

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