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<p>This paper presents sharp lower bounds for the area functional for planar regular homeomorphisms with the Lusin (<i>N</i>)-property, under specific growth restrictions on the <i>p</i>-angular dilatation (<InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11785_2025_1787_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="71" /> </InlineMediaObject> <EquationSource Format="TEX">\(1&lt;p&lt;2\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>1</mn> <mo>&lt;</mo> <mi>p</mi> <mo>&lt;</mo> <mn>2</mn> </mrow> </math></EquationSource> </InlineEquation>). We further demonstrate the application of these novel bounds in analyzing the asymptotic behavior at the origin of regular homeomorphic solutions to the nonlinear Beltrami equation.</p>

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Sharp lower bounds for area distortion via growth control of angular dilatations

  • 期刊论文

  • 发表日期：

    2025年8月12日

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  • I. Petkov,
  • R. Salimov,
  • M. Stefanchuk

摘要

This paper presents sharp lower bounds for the area functional for planar regular homeomorphisms with the Lusin (N)-property, under specific growth restrictions on the p-angular dilatation ( \(1<p<2\) 1 < p < 2 ). We further demonstrate the application of these novel bounds in analyzing the asymptotic behavior at the origin of regular homeomorphic solutions to the nonlinear Beltrami equation.