Stability of flat-core pinned p-elasticae

TL;DR

This paper classifies the stability of flat-core p-elasticae in Euclidean space under pinned boundary conditions, completing the stability classification for all p in (1,∞) and dimensions d ≥ 2.

Contribution

It provides a comprehensive stability classification of flat-core p-elasticae, extending previous work to all p and dimensions, thus completing the overall classification.

Findings

Complete stability classification for flat-core p-elasticae

Extension of previous results to all p in (1,∞)

Results applicable in dimensions d ≥ 2

Abstract

We classify the stability of flat-core $p$-elasticae in $\mathbf{R}^d$ subject to the pinned boundary condition. Together with previous work, this completes the classification of stable pinned $p$-elasticae in $\mathbf{R}^d$ for all $p\in(1,\infty)$ and $d\geq2$.