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<p>In this paper, we establish the global Hölder gradient estimate for solutions to the Dirichlet problem of the Monge-Ampère equation <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="208_2025_3250_Article_IEq4.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="90" /> </InlineMediaObject> <EquationSource Format="TEX">\(\det D^2u = f\)</EquationSource> </InlineEquation> on strictly convex but not uniformly convex domain <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="208_2025_3250_Article_IEq5.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(\Omega\)</EquationSource> </InlineEquation>.</p>

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Global \(C^{1,\alpha }\) regularity for Monge-Ampère equations on planar convex domains

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年8月25日

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  • Qing Han,
  • Jiakun Liu,
  • Yang Zhou

摘要

In this paper, we establish the global Hölder gradient estimate for solutions to the Dirichlet problem of the Monge-Ampère equation \(\det D^2u = f\) on strictly convex but not uniformly convex domain \(\Omega\) .