A family of interaction energy minimizers supported on two intervals

Steven B. Damelin, Ruiwen Shu

In this paper, we consider the one-dimensional interaction energy $\frac{1}{2}{\int }_{\mathbb{R}}(W\ast \rho )(x)d\rho (x)+{\int }_{\mathbb{R}}U(x)d\rho (x)$ where the interaction potential $W(x)= -\…