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<p>We show that the fundamental tone of the bilaplacian with Dirichlet or Navier boundary conditions on radially symmetric domains is always simple in dimension <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(N\ge 3\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>N</mi> <mo>≥</mo> <mn>3</mn> </mrow> </math></EquationSource> </InlineEquation>. In dimension <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(N=2\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>N</mi> <mo>=</mo> <mn>2</mn> </mrow> </math></EquationSource> </InlineEquation>, we show that it is simple if the inner radius is sufficiently close to the outer one.</p>

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ON THE EIGENVALUES OF THE BIHARMONIC OPERATOR ON ANNULI

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年12月3日

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  • Davide Buoso,
  • Riccardo Molinarolo

摘要

We show that the fundamental tone of the bilaplacian with Dirichlet or Navier boundary conditions on radially symmetric domains is always simple in dimension \(N\ge 3\) N ≥ 3 . In dimension \(N=2\) N = 2 , we show that it is simple if the inner radius is sufficiently close to the outer one.