Mappings of L p -integrable distortion: regularity of the inverse
Onninen, J., & Tengvall, V. (2016). Mappings of L p -integrable distortion: regularity of the inverse. Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 146 (3), 647-663. doi:10.1017/S0308210515000530
© Royal Society of Edinburgh 2016. This is a final draft version of an article whose final and definitive form has been published by Royal Society of Edinburgh. Published in this repository with the kind permission of the publisher.
Let X be an open set in R n and suppose that f : X → R n is a Sobolev homeomorphism. We study the regularity of f −1 under the L p -integrability assumption on the distortion function Kf . First, if X is the unit ball and p > n−1, then the optimal local modulus of continuity of f −1 is attained by a radially symmetric mapping. We show that this is not the case when p 6 n − 1 and n > 3, and answer a question raised by S. Hencl and P. Koskela. Second, we obtain the optimal integrability results for |Df −1 | in terms of the L p -integrability assumptions of Kf .