Periodic energy minimizers for a one-dimensional liquid drop model
Rupert L. Frank, Elliott H. Lieb
TL;DR
This paper revisits and extends the proof of periodicity of energy minimizers in a one-dimensional liquid drop model, applicable to various boundary conditions and charge neutrality scenarios.
Contribution
It provides a new, more general proof of periodicity for minimizers, broadening the applicability beyond previous results.
Findings
Periodic minimizers exist under general boundary conditions.
The proof applies to both neutral and non-neutral cases.
The result confirms the structure of minimizers in the model.
Abstract
We reprove a result by Ren and Wei concerning the periodicity of minimizers of a one-dimensional liquid drop model in the neutral case. Our proof works for general boundary conditions and also in the non-neutral case.
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