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Existence and Stability for a Non-Local Isoperimetric Model of Charged Liquid Drops

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Abstract

We consider a variational problem related to the shape of charged liquid drops at equilibrium. We show that this problem never admits local minimizers with respect to L 1 perturbations preserving the volume. However, we prove that the ball is stable under small C 1,1 perturbations when the charge is small enough.

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Authors and Affiliations

  1. Max-Planck-Institut für Mathematik, Inselstrasse 22, 04103, Leipzig, Germany

    Michael Goldman

  2. Department of Mathematics, University of Pisa, Largo Bruno Pontecorvo 5, 56127, Pisa, Italy

    Matteo Novaga

  3. Scuola Normale Superiore di Pisa, Piazza dei Cavalieri 4, 56126, Pisa, Italy

    Berardo Ruffini

Authors
  1. Michael Goldman
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  2. Matteo Novaga
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  3. Berardo Ruffini
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Correspondence to Matteo Novaga.

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Communicated by A. Braides

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Goldman, M., Novaga, M. & Ruffini, B. Existence and Stability for a Non-Local Isoperimetric Model of Charged Liquid Drops. Arch Rational Mech Anal 217, 1–36 (2015). https://doi.org/10.1007/s00205-014-0827-9

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  • DOI: https://doi.org/10.1007/s00205-014-0827-9

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