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<p>Let <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\Omega \)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="normal">Ω</mi> </math></EquationSource> </InlineEquation> be a bounded, smooth domain of <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\mathbb {R}^N\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mi>N</mi> </msup> </math></EquationSource> </InlineEquation>, <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(N\ge 2\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>N</mi> <mo>≥</mo> <mn>2</mn> </mrow> </math></EquationSource> </InlineEquation>. In this paper, we prove some inequalities involving the first Robin eigenvalue of the <i>p</i>-laplacian operator. In particular, we prove an upper bound for the first Robin eigenvalue of nonlinear elliptic operators in terms of the first Dirichlet eigenvalue.</p>

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Upper and Lower Bounds for the First Robin Eigenvalue of Nonlinear Elliptic Operators

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年2月25日

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  • Rosa Barbato,
  • Francesco Della Pietra

摘要

Let \(\Omega \) Ω be a bounded, smooth domain of \(\mathbb {R}^N\) R N , \(N\ge 2\) N ≥ 2 . In this paper, we prove some inequalities involving the first Robin eigenvalue of the p-laplacian operator. In particular, we prove an upper bound for the first Robin eigenvalue of nonlinear elliptic operators in terms of the first Dirichlet eigenvalue.