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<p>In this paper , we introduce a principal value singular integral operator related to the well-known Lamé–Navier system on a simple closed Lyapunov curve <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\gamma \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>γ</mi> </math></EquationSource> </InlineEquation> of <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\({{\mathbb {R}}}^2\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mn>2</mn> </msup> </math></EquationSource> </InlineEquation>. We prove that the higher-order Lipschitz class <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\text{ Lip }(\gamma , 1+\nu )\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mspace width="0.333333em" /> <mtext>Lip</mtext> <mspace width="0.333333em" /> <mo stretchy="false">(</mo> <mi>γ</mi> <mo>,</mo> <mn>1</mn> <mo>+</mo> <mi>ν</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> behaves invariant under the action of that singular integral operator.</p>

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A Plemelj–Privalov Theorem for the Plane Lamé–Navier System

  • 期刊论文

  • 发表日期：

    2026年5月12日

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  • Diego Esteban Gutierrez Valencia,
  • Ricardo Abreu Blaya,
  • Daniel Alfonso Santiesteban,
  • Yudier Peña Pérez

摘要

In this paper , we introduce a principal value singular integral operator related to the well-known Lamé–Navier system on a simple closed Lyapunov curve \(\gamma \) γ of \({{\mathbb {R}}}^2\) R 2 . We prove that the higher-order Lipschitz class \(\text{ Lip }(\gamma , 1+\nu )\) Lip ( γ , 1 + ν ) behaves invariant under the action of that singular integral operator.