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An isoperimetric problem with Coulomb repulsion and attraction to a background nucleus

Publication ,  Journal Article
Lu, J; Otto, F
August 28, 2015

We study an isoperimetric problem the energy of which contains the perimeter of a set, Coulomb repulsion of the set with itself, and attraction of the set to a background nucleus as a point charge with charge $Z$. For the variational problem with constrained volume $V$, our main result is that the minimizer does not exist if $V - Z$ is larger than a constant multiple of $\max(Z^{2/3}, 1)$. The main technical ingredients of our proof are a uniform density lemma and electrostatic screening arguments.

Duke Scholars

Publication Date

August 28, 2015
 

Publication Date

August 28, 2015