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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2020
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2005.06559 |
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| _version_ | 1866917005424066560 |
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| author | Doležalová, Anna Hrubešová, Marika Roskovec, Tomáš |
| author_facet | Doležalová, Anna Hrubešová, Marika Roskovec, Tomáš |
| contents | It is well-known that there is a Sobolev homeomorphism $f\in W^{1,p}([-1,1]^n,[-1,1]^n)$ for any $p<n$ which maps a set $C$ of zero Lebesgue $n$-dimensional measure onto the set of positive measure. We study the size of this critical set $C$ and characterize its lower and upper bounds from the perspective of Hausdorff measures defined by a general gauge function. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2005_06559 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Hausdorff measure of critical set for Luzin $N$ condition Doležalová, Anna Hrubešová, Marika Roskovec, Tomáš Functional Analysis 46E35 It is well-known that there is a Sobolev homeomorphism $f\in W^{1,p}([-1,1]^n,[-1,1]^n)$ for any $p<n$ which maps a set $C$ of zero Lebesgue $n$-dimensional measure onto the set of positive measure. We study the size of this critical set $C$ and characterize its lower and upper bounds from the perspective of Hausdorff measures defined by a general gauge function. |
| title | Hausdorff measure of critical set for Luzin $N$ condition |
| topic | Functional Analysis 46E35 |
| url | https://arxiv.org/abs/2005.06559 |