Regularity of the inverse of a planar Sobolev homeomorphism

Abstract

Let $\Omega\subset{\er}^2$ be a domain. If $f\in W^{1,1}_{\loc}(\Omega,\er^2)$ is a homeomorphism of finite distortion, we show that $f^{-1}\in W^{1,1}_{\loc}(f(\Omega),\er^2)$ and that $f^{-1}$ has finite distortion.

Keywords

• Regularity
• inverse
• planar
• Sobolev
• homeomorphism