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<p>For a non-empty, bounded, open, and convex set of class <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(C^2\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>C</mi> <mn>2</mn> </msup> </math></EquationSource> </InlineEquation>, we consider the Torsional Rigidity associated to the <i>k</i>-Hessian operator. We first prove Pólya type lower bound for the <i>k</i>-Torsional Rigidity in any dimension; then, in order to investigate optimal sets in the Pólya type inequality, we provide two quantitative estimates. We finally prove an upper bound for the eigenvalue of the <i>k</i>-Hessian operator.</p>

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Some Shape Functionals for the k-Hessian Equation

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年4月8日

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  • Alba Lia Masiello,
  • Francesco Salerno

摘要

For a non-empty, bounded, open, and convex set of class \(C^2\) C 2 , we consider the Torsional Rigidity associated to the k-Hessian operator. We first prove Pólya type lower bound for the k-Torsional Rigidity in any dimension; then, in order to investigate optimal sets in the Pólya type inequality, we provide two quantitative estimates. We finally prove an upper bound for the eigenvalue of the k-Hessian operator.