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<p>We establish the area formula for change-of-variable mappings in the Sobolev space <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(W^{k,p}_{\text {loc}}\)</EquationSource> <EquationSource Format="MATHML"><math> <msubsup> <mi>W</mi> <mtext>loc</mtext> <mrow> <mi>k</mi> <mo>,</mo> <mi>p</mi> </mrow> </msubsup> </math></EquationSource> </InlineEquation>. Our approach relies on constructing Lipschitz approximations of Sobolev functions that agree with the original functions outside a set of Riesz capacity zero.</p>

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THE REFINED AREA FORMULA FOR SOBOLEV MAPPINGS \(W^{k,p}\)

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年9月20日

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  • Paz Hashash

摘要

We establish the area formula for change-of-variable mappings in the Sobolev space \(W^{k,p}_{\text {loc}}\) W loc k , p . Our approach relies on constructing Lipschitz approximations of Sobolev functions that agree with the original functions outside a set of Riesz capacity zero.