Geodesic
Variation of quasiconformal mappings on lines
Leonid V. Kovalev1 ; Jani Onninen1
1 Department of Mathematics Syracuse University 215 Carnegie Syracuse, NY 13244, U.S.A.
Studia Mathematica, Tome 195 (2009) no. 3, pp. 257-274

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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 $p=1$.
DOI : 10.4064/sm195-3-5
Keywords: obtain improved regularity homeomorphic solutions reduced beltrami equation compared standard beltrami equation improvement possible terms lder sobolev regularity instead results concern generalized variation restrictions lines specifically prove restriction line segment has finite p variation necessarily

Leonid V. Kovalev 1 ; Jani Onninen 1

1 Department of Mathematics Syracuse University 215 Carnegie Syracuse, NY 13244, U.S.A. 
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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

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