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

Michael Goldman; Matteo Novaga; Berardo Ruffini

doi:10.1007/s00205-014-0827-9

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

Michael Goldman
, Matteo Novaga
, Berardo Ruffini

Max Planck Institute for Mathematics in the Sciences
Dipartimento di Matematica
University of Pisa
Scuola Normale Superiore di Pisa

Research output: Contribution to journal › Article › peer-review

33 Citations (Scopus)

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 L¹ perturbations preserving the volume. However, we prove that the ball is stable under small C^1,1 perturbations when the charge is small enough.

Original language	English
Pages (from-to)	1-36
Number of pages	36
Journal	Archive for Rational Mechanics and Analysis
Volume	217
Issue number	1
DOIs	https://doi.org/10.1007/s00205-014-0827-9
Publication status	Published - 1 Jul 2015
Externally published	Yes

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title = "Existence and Stability for a Non-Local Isoperimetric Model of Charged Liquid Drops",

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 L1 perturbations preserving the volume. However, we prove that the ball is stable under small C1,1 perturbations when the charge is small enough.",

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AB - 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 L1 perturbations preserving the volume. However, we prove that the ball is stable under small C1,1 perturbations when the charge is small enough.

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

Abstract

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