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On a Uniqueness Property of Harmonic Functions

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Abstract

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.

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Authors and Affiliations

  1. Department of Mathematics & Statistics, University of South Florida, 4202 East Fowler Avenue, PHY 114, Tampa, FL, 33620-5700, USA

    Dmitry Khavinson

  2. Department of Mathematics, Royal Institute of Technology, Stockholm, S-10044, Sweden

    Harold S. Shapiro

Authors
  1. Dmitry Khavinson
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  2. Harold S. Shapiro
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Corresponding author

Correspondence to Dmitry Khavinson.

Additional information

The first author gratefully acknowledges partial support from the National Science Foundation under grants DMS-0139008 and DMS-0701873.

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Khavinson, D., Shapiro, H.S. On a Uniqueness Property of Harmonic Functions. Comput. Methods Funct. Theory 8, 143–150 (2008). https://doi.org/10.1007/BF03321677

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  • DOI: https://doi.org/10.1007/BF03321677

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