Calculus of Variations and Geometric Measure Theory

M. Bonacini - H. Knüpfer - M. Röger

Optimal distribution of oppositely charged phases: perfect screening and other properties

created by bonacini on 12 May 2015
modified on 08 Jan 2016


Accepted Paper

Inserted: 12 may 2015
Last Updated: 8 jan 2016

Journal: SIAM J. Math. Anal.
Year: 2015


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.