Let be a mapping of finite distortion, where . Assume that the distortion function satisfies for some . We establish optimal regularity and area distortion estimates for f. In particular, we prove that for every . This answers positively, in dimension , the well-known conjectures of Iwaniec and Sbordone [T. Iwaniec, C. Sbordone, Quasiharmonic fields, Ann. Inst. H. Poincaré Anal. Non Linéaire 18 (2001) 519–572, Conjecture 1.1] and of Iwaniec, Koskela and Martin [T. Iwaniec, P. Koskela, G. Martin, Mappings of BMO-distortion and Beltrami-type operators, J. Anal. Math. 88 (2002) 337–381, Conjecture 7.1].
@article{AIHPC_2010__27_1_1_0, author = {Astala, Kari and Gill, James T. and Rohde, Steffen and Saksman, Eero}, title = {Optimal regularity for planar mappings of finite distortion}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, pages = {1--19}, publisher = {Elsevier}, volume = {27}, number = {1}, year = {2010}, doi = {10.1016/j.anihpc.2009.01.012}, zbl = {1191.30007}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.anihpc.2009.01.012/} }
TY - JOUR AU - Astala, Kari AU - Gill, James T. AU - Rohde, Steffen AU - Saksman, Eero TI - Optimal regularity for planar mappings of finite distortion JO - Annales de l'I.H.P. Analyse non linéaire PY - 2010 SP - 1 EP - 19 VL - 27 IS - 1 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.anihpc.2009.01.012/ DO - 10.1016/j.anihpc.2009.01.012 LA - en ID - AIHPC_2010__27_1_1_0 ER -
%0 Journal Article %A Astala, Kari %A Gill, James T. %A Rohde, Steffen %A Saksman, Eero %T Optimal regularity for planar mappings of finite distortion %J Annales de l'I.H.P. Analyse non linéaire %D 2010 %P 1-19 %V 27 %N 1 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.anihpc.2009.01.012/ %R 10.1016/j.anihpc.2009.01.012 %G en %F AIHPC_2010__27_1_1_0
Astala, Kari; Gill, James T.; Rohde, Steffen; Saksman, Eero. Optimal regularity for planar mappings of finite distortion. Annales de l'I.H.P. Analyse non linéaire, Tome 27 (2010) no. 1, pp. 1-19. doi : 10.1016/j.anihpc.2009.01.012. http://www.numdam.org/articles/10.1016/j.anihpc.2009.01.012/
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