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Two-phase quadrature domains

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Abstract

Recent work on two-phase free boundary problems has led to the investigation of a new type of quadrature domain for harmonic functions. This paper develops a method of constructing such quadrature domains based on the technique of partial balayage, which has proved to be a useful tool in the study of one-phase quadrature domains and Hele-Shaw flows.

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Authors and Affiliations

  1. School of Mathematical Sciences, University College Dublin, Belfield, Dublin 4, Ireland

    Stephen J. Gardiner

  2. Department of Mathematics, Linköping University, 581 83, Linköping, Sweden

    Tomas Sjödin

Authors
  1. Stephen J. Gardiner
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  2. Tomas Sjödin
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Corresponding author

Correspondence to Stephen J. Gardiner.

Additional information

This research is part of the programme of the ESF Network “Harmonic and Complex Analysis and Applications” (HCAA).

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Gardiner, S.J., Sjödin, T. Two-phase quadrature domains. JAMA 116, 335–354 (2012). https://doi.org/10.1007/s11854-012-0009-3

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  • DOI: https://doi.org/10.1007/s11854-012-0009-3

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