Wikibooks

Harmonic Function Theory

Contents

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  1. Holomorphic functions and harmonic functions
  2. Mean value properties, Poisson's formula
  3. Liouville's theorem, Harnack's inequality, Cauchy estimates
  4. Isolated singularities
  5. Uniform limits, Harnack's principle
  6. Differentiability and analyticity
  7. Extremum principles
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