Optimal regularity for planar mappings of finite distortion
| dc.creator | Astala, Kari | |
| dc.creator | Gill, James | |
| dc.creator | Rohde, Steffen | |
| dc.creator | Saksman, Eero | |
| dc.date | 2008-01-30 | |
| dc.date | 2009-02-12 | |
| dc.date.accessioned | 2026-07-07T12:40:08Z | |
| dc.date.available | 2026-07-07T12:40:08Z | |
| dc.description | Let $f:Ω\to\IR^2$ be a mapping of finite distortion, where $Ω\subset\IR^2 .$ Assume that the distortion function $K(x,f)$ satisfies $e^{K(\cdot, f)}\in L^p_{loc}(Ω)$ for some $p>0.$ We establish optimal regularity and area distortion estimates for $f$. Especially, we prove that $|Df|^2 \log^{β-1}(e + |Df|) \in L^1_{loc}(Ω) $ for every $β<p.$ This answers positively well known conjectures due to Iwaniec and Martin \cite{IMbook} and to Iwaniec, Koskela and Martin \cite{IKM}. | |
| dc.description | 22 pages, formula (3) has been corrected | |
| dc.identifier | https://arxiv.org/abs/0801.4624 | |
| dc.identifier | http://arxiv.org/abs/0801.4624 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/219355 | |
| dc.subject | Complex Variables | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 30C62, 35J45 | |
| dc.title | Optimal regularity for planar mappings of finite distortion | |
| dc.type | text |