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<p>We prove that the Robin eigenfunctions on convex domains of <InlineEquation ID="IEq3"> <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> are <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(H^2\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>H</mi> <mn>2</mn> </msup> </math></EquationSource> </InlineEquation>-regular regardless of the sign of the parameter involved in the boundary conditions. The proof is an adaptation of a classical argument used in the case of positive parameters combined with a Rellich-Pohozaev identity.</p>

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\(H^2\)-REGULARITY ON CONVEX DOMAINS FOR ROBIN EIGENFUNCTIONS WITH PARAMETER OF ARBITRARY SIGN

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年11月15日

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  • Pier Domenico Lamberti,
  • Luigi Provenzano

摘要

We prove that the Robin eigenfunctions on convex domains of \(\mathbb {R}^n\) R n are \(H^2\) H 2 -regular regardless of the sign of the parameter involved in the boundary conditions. The proof is an adaptation of a classical argument used in the case of positive parameters combined with a Rellich-Pohozaev identity.