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<p>We study the relationship between Sobolev extension domains and homogeneous Sobolev extension domains. Precisely, for a certain range of exponents <i>p</i> and <i>q</i>, we construct a <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\((W^{1, p}, W^{1, q})\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <msup> <mi>W</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>p</mi> </mrow> </msup> <mo>,</mo> <msup> <mi>W</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>q</mi> </mrow> </msup> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>-extension domain which is not an <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\((L^{1, p}, L^{1, q})\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <msup> <mi>L</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>p</mi> </mrow> </msup> <mo>,</mo> <msup> <mi>L</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>q</mi> </mrow> </msup> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>-extension domain.</p>

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Sobolev versus homogeneous Sobolev extension II

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年3月18日

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  • Pekka Koskela,
  • Riddhi Mishra,
  • Zheng Zhu

摘要

We study the relationship between Sobolev extension domains and homogeneous Sobolev extension domains. Precisely, for a certain range of exponents p and q, we construct a \((W^{1, p}, W^{1, q})\) ( W 1 , p , W 1 , q ) -extension domain which is not an \((L^{1, p}, L^{1, q})\) ( L 1 , p , L 1 , q ) -extension domain.