On a Uniqueness Property of Harmonic Functions

  • Dmitry Khavinson
  • Harold S. Shapiro


We investigate the problem of uniqueness for functions u harmonic in a domain Ω and vanishing on some parts of the intersection (not necessarily connected) of Ω with a line m. It turns out that for some configurations u must vanish on the whole intersection of m and Ω, but this is not always the case. Generalizations to solutions of more general analytic elliptic equations are discussed as well.


Analytic continuation harmonic functions cells of harmonicity Schwarz reflection principle 

2000 MSC

31A35 35A20 31A05 


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Copyright information

© Heldermann  Verlag 2008

Authors and Affiliations

  1. 1.Department of Mathematics & StatisticsUniversity of South FloridaTampaUSA
  2. 2.Department of MathematicsRoyal Institute of TechnologyStockholmSweden

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