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Harmonic Functions

  • John B. Conway
Chapter
  • 5.2k Downloads
Part of the Graduate Texts in Mathematics book series (GTM, volume 11)

Abstract

In this chapter harmonic functions will be studied and the Dirichlet Problem will be solved. The Dirichlet Problem consists in determining all regions G such that for any continuous function f: ∂G → ℝ there is a continuous function u:G-→ ℝ such that u(z) = f(z) for z in ∂G and u is harmonic in G. Alternately, we are asked to determine all regions G such that Laplace’s Equation is solvable with arbitrary boundary values.

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Copyright information

© Springer Science+Business Media, Inc. 1978

Authors and Affiliations

  • John B. Conway
    • 1
  1. 1.Mathematics DepartmentUniversity of TennesseeKnoxvilleUSA

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