Calculus of Variations and Geometric Measure Theory
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Optimal distribution of oppositely charged phases: Screening, charge neutrality and regularity

Hans Knüpfer

created by gelli on 31 Jan 2016

12 feb 2016 -- 11:30   [open in google calendar]

Aula Magna (Dipartimento di Matematica di Pisa)

Abstract.

We study the minimum energy configuration of a uniform distribution of negative charge subject to Coulomb repulsive self-interaction and attractive interaction with a fixed positively charged domain. After having established existence and uniqueness of a minimizing configuration, we prove charge neutrality and the complete screening of the Coulomb potential exerted by the positive charge, and we discuss the regularity properties of the solution. We also determine, in the variational sense of Gamma-convergence, the limit model when the charge density of the negative phase is much higher than the positive one. This is joint work with M. Bonacini and M. Röger.

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