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<p>In this paper, we establish a trace Moser-Trudinger inequality on a compact Riemann surface <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40304_2024_415_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(\Sigma \)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="normal">Σ</mi> </math></EquationSource> </InlineEquation> with corners on <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40304_2024_415_Article_IEq2.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="23" /> </InlineMediaObject> <EquationSource Format="TEX">\(\partial \Sigma \)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>∂</mi> <mi mathvariant="normal">Σ</mi> </mrow> </math></EquationSource> </InlineEquation>. It is also regarded as “trace imbedding inequality” when the boundary carries the conical sigularities. Besides, based on blow-up analysis, we prove the existence of extremal functions for this trace Moser-Trudinger inequality.</p>

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A trace Moser-Trudinger inequality on compact Riemannian surface with corners on its boundary

  • 期刊论文

  • 发表日期：

    2025年4月3日

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  • Tao Zhang,
  • Chunqin Zhou,
  • Xiaobao Zhu

摘要

In this paper, we establish a trace Moser-Trudinger inequality on a compact Riemann surface \(\Sigma \) Σ with corners on \(\partial \Sigma \) ∂ Σ . It is also regarded as “trace imbedding inequality” when the boundary carries the conical sigularities. Besides, based on blow-up analysis, we prove the existence of extremal functions for this trace Moser-Trudinger inequality.