Scholarlink

<p>We define a relaxed version <i>H</i><Stack> <sub><i>f</i></sub> <sup>fine</sup> </Stack> of the distortion number <i>H</i><sub><i>f</i></sub> that is used to define quasiconformal mappings. Then we show that for a BV function <i>f</i> ∈ BV(ℝ<sup><i>n</i></sup>;ℝ<sup><i>n</i></sup>), for ∣<i>Df</i>∣-a.e. <i>x</i> ∈ ℝ<sup><i>n</i></sup> it holds that <i>H</i><Stack> <sub><i>f</i>*</sub> <sup>fine</sup> </Stack>(<i>x</i>) &lt; ∞ if and only if <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\({{dDf}\over{d|{Df}|}}(x)\)</EquationSource> <EquationSource Format="MATHML"><math display="block"> <mrow> <mfrac> <mrow> <mi>d</mi> <mi>D</mi> <mi>f</mi> </mrow> <mrow> <mi>d</mi> <mrow> <mo stretchy="false">|</mo> </mrow> <mrow> <mi>D</mi> <mi>f</mi> </mrow> <mrow> <mo stretchy="false">|</mo> </mrow> </mrow> </mfrac> </mrow> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> </math></EquationSource> </InlineEquation> has full rank.</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

Quasiconformal mappings and the rank of \({{dDf}\over{d|{Df}|}}\) for f ∈ BV(ℝn;ℝn)

  • 期刊论文

  • 发表日期：

    2025年12月3日

查看全文
  • Panu Lahti

摘要

We define a relaxed version H f fine of the distortion number Hf that is used to define quasiconformal mappings. Then we show that for a BV function f ∈ BV(ℝn;ℝn), for ∣Df∣-a.e. x ∈ ℝn it holds that H f* fine (x) < ∞ if and only if \({{dDf}\over{d|{Df}|}}(x)\) d D f d | D f | ( x ) has full rank.