We obtain improved regularity of homeomorphic solutions of the reduced Beltrami equation, as compared to the standard Beltrami equation. Such an improvement is not possible in terms of Hölder or Sobolev regularity; instead, our results concern the generalized variation of restrictions to lines. Specifically, we prove that the restriction to any line segment has finite p-variation for all p > 1 but not necessarily for p = 1.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm195-3-5,
author = {Leonid V. Kovalev and Jani Onninen},
title = {Variation of quasiconformal mappings on lines},
journal = {Studia Mathematica},
volume = {192},
year = {2009},
pages = {257-274},
zbl = {1178.30023},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm195-3-5}
}
Leonid V. Kovalev; Jani Onninen. Variation of quasiconformal mappings on lines. Studia Mathematica, Tome 192 (2009) pp. 257-274. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm195-3-5/