Pointwise rotation for homeomorphisms with integrable distortion and controlled compression
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
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2021
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| _version_ | 1866914213123850240 |
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| author | Hitruhin, Lauri Sengupta, Banhirup |
| author_facet | Hitruhin, Lauri Sengupta, Banhirup |
| contents | We obtain sharp rotation bounds for homeomorphisms $f:\mathbb{C}\to\mathbb{C}$ whose distortion is in $L^p_{loc}$, $p\geq1$, and whose inverse have controlled modulus of continuity. The motivation to study this class of maps comes from so-called Yudovich solutions to planar Euler equations. Furthermore, we present examples proving sharpness in a strong sense, thereby settling the borderline case $p=1$ in \cite[Theorem 3]{CHS}. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2110_12809 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Pointwise rotation for homeomorphisms with integrable distortion and controlled compression Hitruhin, Lauri Sengupta, Banhirup Dynamical Systems Analysis of PDEs Complex Variables 30C62(Primary), 35Q31(Secondary) We obtain sharp rotation bounds for homeomorphisms $f:\mathbb{C}\to\mathbb{C}$ whose distortion is in $L^p_{loc}$, $p\geq1$, and whose inverse have controlled modulus of continuity. The motivation to study this class of maps comes from so-called Yudovich solutions to planar Euler equations. Furthermore, we present examples proving sharpness in a strong sense, thereby settling the borderline case $p=1$ in \cite[Theorem 3]{CHS}. |
| title | Pointwise rotation for homeomorphisms with integrable distortion and controlled compression |
| topic | Dynamical Systems Analysis of PDEs Complex Variables 30C62(Primary), 35Q31(Secondary) |
| url | https://arxiv.org/abs/2110.12809 |