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<p>In this paper we study <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12220_2025_2113_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="30" /> </InlineMediaObject> <EquationSource Format="TEX">\(C^{1, 1}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>C</mi> <mrow> <mn>1</mn> <mo>,</mo> <mn>1</mn> </mrow> </msup> </math></EquationSource> </InlineEquation> estimates for solutions to the degenerate Gauss image Problem, which is proposed by Boroczky-Lutwak-Yang-Zhang-Zhao as a generalization of the Aleksandrov problem. Under some sufficient conditions, we obtain an existence result to the degenerate Gauss image Problem based on the a priori estimates for solutions to the corresponding degenerate Monge-Ampère type equations.</p>

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C1, 1 Estimates for Solutions to the Degenerate Gauss Image Problem

  • 期刊论文

  • 发表日期：

    2025年7月24日

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  • Qiang Tu

摘要

In this paper we study \(C^{1, 1}\) C 1 , 1 estimates for solutions to the degenerate Gauss image Problem, which is proposed by Boroczky-Lutwak-Yang-Zhang-Zhao as a generalization of the Aleksandrov problem. Under some sufficient conditions, we obtain an existence result to the degenerate Gauss image Problem based on the a priori estimates for solutions to the corresponding degenerate Monge-Ampère type equations.