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<p>We show that the volume of the boundary of a bounded Sobolev (<i>p</i>,&#xa0;<i>q</i>)-extension domain is zero when <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="526_2025_2934_Article_IEq1.gif" Format="GIF" Height="24" Rendition="HTML" Resolution="72" Type="Linedraw" Width="133" /> </InlineMediaObject> <EquationSource Format="TEX">\(1\le q&lt;p&lt; \frac{qn}{(n-q)}.\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>1</mn> <mo>≤</mo> <mi>q</mi> <mo>&lt;</mo> <mi>p</mi> <mo>&lt;</mo> <mfrac> <mrow> <mi mathvariant="italic">qn</mi> </mrow> <mrow> <mo stretchy="false">(</mo> <mi>n</mi> <mo>-</mo> <mi>q</mi> <mo stretchy="false">)</mo> </mrow> </mfrac> <mo>.</mo> </mrow> </math></EquationSource> </InlineEquation></p>

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The volume of the boundary of a Sobolev (p, q)-extension domain II

  • 期刊论文

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  • 发表日期：

    2025年2月17日

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  • Pekka Koskela,
  • Riddhi Mishra

摘要

We show that the volume of the boundary of a bounded Sobolev (p, q)-extension domain is zero when \(1\le q<p< \frac{qn}{(n-q)}.\) 1 ≤ q < p < qn ( n - q ) .