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<p>In this paper, we introduce a singular integral operator related to the well-known Lamé–Navier system in the unit disk of <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\({{\mathbb {R}}}^2.\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mn>2</mn> </msup> <mo>.</mo> </mrow> </math></EquationSource> </InlineEquation> We prove that the higher order Lipschitz classes (of order <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(1+\nu \)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>1</mn> <mo>+</mo> <mi>ν</mi> </mrow> </math></EquationSource> </InlineEquation>) behave invariant under the action of that operator.</p>

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A singular integral operator for the Lamé–Navier system in the unit disk

  • 期刊论文

  • 发表日期：

    2025年11月26日

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  • Diego Esteban Gutierrez Valencia,
  • Ricardo Abreu Blaya,
  • Martín Patricio Árciga Alejandre,
  • Yudier Peña Pérez

摘要

In this paper, we introduce a singular integral operator related to the well-known Lamé–Navier system in the unit disk of \({{\mathbb {R}}}^2.\) R 2 . We prove that the higher order Lipschitz classes (of order \(1+\nu \) 1 + ν ) behave invariant under the action of that operator.