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<p>We classify the stability of flat-core <i>p</i>-elasticae in <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\textbf{R}^d\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi mathvariant="bold">R</mi> <mi>d</mi> </msup> </math></EquationSource> </InlineEquation> subject to the pinned boundary condition. Together with previous work, this completes the classification of stable pinned <i>p</i>-elasticae in <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\textbf{R}^d\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi mathvariant="bold">R</mi> <mi>d</mi> </msup> </math></EquationSource> </InlineEquation> for all <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(p\in (1,\infty )\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>p</mi> <mo>∈</mo> <mo stretchy="false">(</mo> <mn>1</mn> <mo>,</mo> <mi>∞</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(d\ge 2\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>d</mi> <mo>≥</mo> <mn>2</mn> </mrow> </math></EquationSource> </InlineEquation>.</p>

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Stability of flat-core pinned p-elasticae

  • 期刊论文

  • 发表日期：

    2026年2月5日

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  • Tatsuya Miura,
  • Kensuke Yoshizawa

摘要

We classify the stability of flat-core p-elasticae in \(\textbf{R}^d\) R d subject to the pinned boundary condition. Together with previous work, this completes the classification of stable pinned p-elasticae in \(\textbf{R}^d\) R d for all \(p\in (1,\infty )\) p ∈ ( 1 , ∞ ) and \(d\ge 2\) d ≥ 2 .