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<p>This work is devoted to prove an optimum version of the trace inequality associated to the embedding <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13398_2025_1771_Article_IEq4.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="127" /> </InlineMediaObject> <EquationSource Format="TEX">\(BV(\Omega )\subset L^1(\partial \Omega )\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>B</mi> <mi>V</mi> <mrow> <mo stretchy="false">(</mo> <mi mathvariant="normal">Ω</mi> <mo stretchy="false">)</mo> </mrow> <mo>⊂</mo> <msup> <mi>L</mi> <mn>1</mn> </msup> <mrow> <mo stretchy="false">(</mo> <mi>∂</mi> <mi mathvariant="normal">Ω</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation>. Special emphasis is placed on the regularity that the domain <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13398_2025_1771_Article_IEq5.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(\Omega \)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="normal">Ω</mi> </math></EquationSource> </InlineEquation> should exhibit for this result to be valid.</p>

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Trace inequality for \(BV(\Omega )\) in smooth domains

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年8月8日

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  • José C. Sabina de Lis

摘要

This work is devoted to prove an optimum version of the trace inequality associated to the embedding \(BV(\Omega )\subset L^1(\partial \Omega )\) B V ( Ω ) ⊂ L 1 ( ∂ Ω ) . Special emphasis is placed on the regularity that the domain \(\Omega \) Ω should exhibit for this result to be valid.