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<p>In this paper, we introduce Steklov and Neumann isocapacitary constants for the <i>p</i>-Laplacian on compact manifolds. These constants yield two-sided bounds for the <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\((p,\alpha )\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mi>p</mi> <mo>,</mo> <mi>α</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>-Sobolev constants, which degenerate to upper and lower bounds for the first nontrivial Steklov and Neumann eigenvalues of the <i>p</i>-Laplacian when <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\alpha = 1\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>α</mi> <mo>=</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation>.</p>

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Isocapacitary Constants for the p-Laplacian on Compact Manifolds

  • 期刊论文

  • 发表日期：

    2026年7月2日

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  • Lili Wang,
  • Tao Wang

摘要

In this paper, we introduce Steklov and Neumann isocapacitary constants for the p-Laplacian on compact manifolds. These constants yield two-sided bounds for the \((p,\alpha )\) ( p , α ) -Sobolev constants, which degenerate to upper and lower bounds for the first nontrivial Steklov and Neumann eigenvalues of the p-Laplacian when \(\alpha = 1\) α = 1 .