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Séminaire Laurent Schwartz — EDP et applications

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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), Exp. No. 12, 10 p., doi: 10.5802/slsedp.56
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Résumé - Abstract

For the dynamics $x^{\prime \prime } = -\nabla _xV(x)$, an equilibrium point $\underline{x}$ are always unstable when on a neighborhood of $\underline{x}$ the non constant $V$ satisfies $P(x,\partial )V=0$ for a real second order elliptic $P$. The proof uses a result of Kozlov [6].

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