Calculus of Variations and Geometric Measure Theory

S. Daneri - E. Runa

Pattern formation for a local/nonlocal functional arising in colloidal systems

created by daneri on 04 Dec 2020


Published Paper

Inserted: 4 dec 2020

Journal: SIAM Journal Math. Anal.
Year: 2020

ArXiv: 1810.11884 PDF


In this paper we study pattern formation for a physical localnonlocal interaction functional where the local attractive term is given by the $1$-perimeter and the nonlocal repulsive term is the Yukawa (or screened Coulomb) potential. This model is physically interesting as it is the $\Gamma$-limit of a double Yukawa model used to explain and simulate pattern formation in colloidal systems. Following a strategy introduced in~\cite{Daneri-Runa ARMA} we prove that in a suitable regime minimizers are periodic stripes, in any space dimension.