## Instability of dielectrics and conductors in electrostatic fields

*Allaire, Grégoire*;

*Rauch, Jeffrey*;

- Publisher: HAL CCSD
- Subject: Dirichlet's Theorem | electromagnetism | [ MATH.MATH-AP ] Mathematics [math]/Analysis of PDEs [math.AP] | Instability | 70H14, 35B35, 35Q60, 35Q61, 35Q70, 70E91 | perfect conductor | [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP] | dielectric | Earnshaw's Theoremarxiv: Physics::Classical Physics

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.

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