EMERGENCE OF NONTRIVIAL MINIMIZERS FOR THE THREE-DIMENSIONAL OHTA–KAWASAKI ENERGY

Document Type

Article

Publication Date

1-1-2020

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.

Identifier

85095333974 (Scopus)

Publication Title

Pure and Applied Analysis

External Full Text Location

https://doi.org/10.2140/paa.2020.2.1

e-ISSN

25785885

ISSN

25785893

First Page

1

Last Page

21

Issue

1

Volume

2

Grant

DMS-1313687

Fund Ref

Università di Pisa

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