Variation of quasiconformal mappings on lines

Leonid V. Kovalev, and Jani Onninen. "Variation of quasiconformal mappings on lines." Studia Mathematica 195.3 (2009): 257-274. <http://eudml.org/doc/284722>.

@article{LeonidV2009,
abstract = {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.},
author = {Leonid V. Kovalev, Jani Onninen},
journal = {Studia Mathematica},
keywords = {quasiconformal mapping; Beltrami equation; quaternions; bounded variation},
language = {eng},
number = {3},
pages = {257-274},
title = {Variation of quasiconformal mappings on lines},
url = {http://eudml.org/doc/284722},
volume = {195},
year = {2009},
}

TY - JOUR
AU - Leonid V. Kovalev
AU - Jani Onninen
TI - Variation of quasiconformal mappings on lines
JO - Studia Mathematica
PY - 2009
VL - 195
IS - 3
SP - 257
EP - 274
AB - 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.
LA - eng
KW - quasiconformal mapping; Beltrami equation; quaternions; bounded variation
UR - http://eudml.org/doc/284722
ER -