Scholarlink

<p>Given <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\alpha \in (0,1)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>α</mi> <mo>∈</mo> <mo stretchy="false">(</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> and a set <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(E\subset \mathbb {R}^N\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>E</mi> <mo>⊂</mo> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mi>N</mi> </msup> </mrow> </math></EquationSource> </InlineEquation> with locally finite fractional <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\alpha \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>α</mi> </math></EquationSource> </InlineEquation>-variation, we show that, for <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(|D^\alpha {\textbf{1}}_E|\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mrow> <mo stretchy="false">|</mo> </mrow> <msup> <mi>D</mi> <mi>α</mi> </msup> <msub> <mn mathvariant="bold">1</mn> <mi>E</mi> </msub> <mrow> <mo stretchy="false">|</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation>-a.e. <i>x</i>, every non-trivial tangent set of <i>E</i> at <i>x</i> with locally finite integer perimeter is a half-space oriented by the fractional inner unit normal of <i>E</i> at <i>x</i>.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

On Blow-ups of Sets with Finite Fractional Variation

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2026年5月11日

查看全文
  • Giorgio Stefani

摘要

Given \(\alpha \in (0,1)\) α ∈ ( 0 , 1 ) and a set \(E\subset \mathbb {R}^N\) E ⊂ R N with locally finite fractional \(\alpha \) α -variation, we show that, for \(|D^\alpha {\textbf{1}}_E|\) | D α 1 E | -a.e. x, every non-trivial tangent set of E at x with locally finite integer perimeter is a half-space oriented by the fractional inner unit normal of E at x.