ACL and differentiability almost everywhere of ring homeomorphisms (Q2901628)
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scientific article; zbMATH DE number 6062169
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | ACL and differentiability almost everywhere of ring homeomorphisms |
scientific article; zbMATH DE number 6062169 |
Statements
31 July 2012
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ring \(Q\)-homeomorphisms
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absolutely continuous on lines
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0.9307193
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0.90813094
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0.89337474
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0.87418914
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0.8693221
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0.8638716
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ACL and differentiability almost everywhere of ring homeomorphisms (English)
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The present article is devoted to the study of mappings introduced by V. Ryazanov, U. Srebro and E. Yakubov, the so-called ring \(Q\)-homeomorphisms, which are a generalization of quasiconformal mappings. It is proved that ring \(Q\)-homeomorphisms in \(\mathbb{R}^n\), \(n\geq 2\), are absolutely continuous on lines, belong to the Sobolev class \(W_{\mathrm {loc}}^{1,1}\) and are differentiable a.e. provided that \(Q\in L^{1}_{\mathrm {loc}}\).
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