Homeomorphisms in the Sobolev space $W^{1,n-1}$

Abstract

We show that each homeomorphism $f\in W^{1,n-1}_{\loc}(\Omega,\rn)$ satisfies $f^{-1}\in BV_{\loc}(f(\Omega),\rn)$. If we moreover assume that $f$ has finite distortion, then $f^{-1}\in W^{1,1}_{\loc}(f(\Omega),\rn)$ and $f^{-1}$ has finite distortion.

Keywords

• Homeomorphisms
• Sobolev
• space
• $W^1,n-1$