Earnshaw’s Theorem in Electrostatics and a Conditional Converse to Dirichlet’s Theorem
Jeffrey Rauch1
1 Department of Mathematics University of Michigan Ann Arbor 48109 MI USA
Séminaire Laurent Schwartz — EDP et applications (2013-2014), Exposé no. 12, 10 p.

For the dynamics x '' =-∇ x V(x), an equilibrium point x ̲ are always unstable when on a neighborhood of x ̲ the non constant V satisfies P(x,∂)V=0 for a real second order elliptic P. The proof uses a result of Kozlov [6].

DOI : 10.5802/slsedp.56
Jeffrey Rauch 1

1 Department of Mathematics University of Michigan Ann Arbor 48109 MI USA 
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Jeffrey Rauch. Earnshaw’s Theorem in Electrostatics and a Conditional Converse to Dirichlet’s Theorem. Séminaire Laurent Schwartz — EDP et applications (2013-2014), Exposé no. 12, 10 p. doi : 10.5802/slsedp.56. https://proceedings.centre-mersenne.org/articles/10.5802/slsedp.56/

[1] G. Allaire and J. Rauch, In preparation.

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