Regularity of the inverse of a Sobolev homeomorphism in space

Abstract

Given a n-dimensional homeomorphism of finite distortion with gradient in the Lorentz space $L^{n-1,1}$, we show that the inversion is a sobolev function of finite distortion. A class of counterexamples demonstrating sharpness of the results is constructed.

Keywords

• Regularity
• inverse
• Sobolev
• homeomorphism
• space