Variation of quasiconformal mappings on lines

• Autorzy: Leonid V. Kovalev , Jani Onninen
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 26A45: Functions of bounded variation, generalizations
• 26B30: Absolutely continuous functions, functions of bounded variation
• 30C62: Quasiconformal mappings in the plane
• 30C65: Quasiconformal mappings in 𝐑 n , other generalizations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2009
• Tom: 195
• Numer: 3
• Strony: 257-274

Daty

wydano

2009

Twórcy

autor

Leonid V. Kovalev

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

autor

Jani Onninen

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

Identyfikatory

DOI

10.4064/sm195-3-5