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{10_4064_sm195_3_5,
author = {Leonid V. Kovalev and Jani Onninen},
title = {Variation of quasiconformal mappings on lines},
journal = {Studia Mathematica},
pages = {257--274},
year = {2009},
volume = {195},
number = {3},
doi = {10.4064/sm195-3-5},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm195-3-5/}
}
TY - JOUR
AU - Leonid V. Kovalev
AU - Jani Onninen
TI - Variation of quasiconformal mappings on lines
JO - Studia Mathematica
PY - 2009
SP - 257
EP - 274
VL - 195
IS - 3
UR - http://geodesic.mathdoc.fr/articles/10.4064/sm195-3-5/
DO - 10.4064/sm195-3-5
LA - en
ID - 10_4064_sm195_3_5
ER -
%0 Journal Article
%A Leonid V. Kovalev
%A Jani Onninen
%T Variation of quasiconformal mappings on lines
%J Studia Mathematica
%D 2009
%P 257-274
%V 195
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4064/sm195-3-5/
%R 10.4064/sm195-3-5
%G en
%F 10_4064_sm195_3_5
Leonid V. Kovalev; Jani Onninen. Variation of quasiconformal mappings on lines. Studia Mathematica, Tome 195 (2009) no. 3, pp. 257-274. doi: 10.4064/sm195-3-5
