Bilipschitz mappings with derivatives of bounded variation

Abstract

Let $\Omega\subset\rn$ be open and suppose that $f:\Omega\to\rn$ is a bilipschitz mapping such that $Df\in BV_{\loc}(\Omega,\er^{n^2})$. We show that under these assumptions the inverse satisfies $Df^{-1}\in BV_{\loc}(f(\Omega),\er^{n^2})$.

Keywords

• Bilipschitz
• mappings
• derivatives
• bounded
• variation