Instability of dielectrics and conductors in electrostatic fields

Grégoire Allaire (1, 2) , Jeffrey Rauch (3)

1 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
2 DeFI - Shape reconstruction and identification
3 Department of Mathematics - University of Michigan

This article proves most of the assertion in §116 of Maxwell's treatise on electromagnetism. The results go under the name Earnshaw's Theorem and assert the absence of stable equilibrium configurations of conductors and dielectrics in an external electrostatic field.

Mots clés: Instability; electromagnetism; dielectric; perfect conductor; Dirichlet's Theorem; Earnshaw's Theorem

Domaines: Equations aux dérivées partielles [math.AP]

Grégoire Allaire, Jeffrey Rauch. Instability of dielectrics and conductors in electrostatic fields. Archive for Rational Mechanics and Analysis, 2017, 124, pp.233-268. ⟨hal-01321566⟩