Annales Academię Scientiarum Fennicę
Mathematica
Volumen 35, 2010, 197-207
Washington University in St. Louis, Department of Mathematics
Campus Box 1146, St. Louis, MO 63130, U.S.A.; jgill 'at' math.wustl.edu
Abstract. Here we answer in the affirmative a conjecture of Iwaniec and Martin from [11] on solutions to the Beltrami equation whose distortion function is sub-exponentially integrable. Namely, we find the sharp Sobolev classes which these maps belong to, as well their area distortion estimates. These methods imply all further integrability results in this logarithmic scale.
2000 Mathematics Subject Classification: Primary 30C62; Secondary 42B20.
Key words: Mappings of finite distortion, sub-exponential distortion, optimal regularity, area distortion.
Reference to this article: J.T. Gill: Planar maps of sub-exponential distortion. Ann. Acad. Sci. Fenn. Math. 35 (2010), 197-207.
doi:10.5186/aasfm.2010.3511
Copyright © 2010 by Academia Scientiarum Fennica