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2020 Emergence of nontrivial minimizers for the three-dimensional Ohta–Kawasaki energy
Hans Knüpfer, Cyrill B. Muratov, Matteo Novaga
Pure Appl. Anal. 2(1): 1-21 (2020). DOI: 10.2140/paa.2020.2.1

Abstract

This paper is concerned with the diffuse interface Ohta–Kawasaki energy in three space dimensions, in a periodic setting, in the parameter regime corresponding to the onset of nontrivial minimizers. We identify the scaling in which a sharp transition from asymptotically trivial to nontrivial minimizers takes place as the small parameter characterizing the width of the interfaces between the two phases goes to zero, while the volume fraction of the minority phases vanishes at an appropriate rate. The value of the threshold is shown to be related to the optimal binding energy solution of Gamow’s liquid drop model of the atomic nucleus. Beyond the threshold the average volume fraction of the minority phase is demonstrated to grow linearly with the distance to the threshold. In addition to these results, we establish a number of properties of the minimizers of the sharp interface screened Ohta–Kawasaki energy in the considered parameter regime. We also establish rather tight upper and lower bounds on the value of the transition threshold.

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Hans Knüpfer. Cyrill B. Muratov. Matteo Novaga. "Emergence of nontrivial minimizers for the three-dimensional Ohta–Kawasaki energy." Pure Appl. Anal. 2 (1) 1 - 21, 2020. https://doi.org/10.2140/paa.2020.2.1

Information

Received: 6 December 2018; Revised: 8 June 2019; Accepted: 16 August 2019; Published: 2020
First available in Project Euclid: 13 December 2019

zbMATH: 07159294
MathSciNet: MR4041275
Digital Object Identifier: 10.2140/paa.2020.2.1

Subjects:
Primary: 34A34 , 35A15 , 35J50
Secondary: 49Q20 , 51P05

Keywords: energy driven pattern formation , Gamma convergence

Rights: Copyright © 2020 Mathematical Sciences Publishers

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