Revistes Catalanes amb Accés Obert (RACO)

Bilipschitz mappings with derivatives of bounded variation

S. Hencl

Resum


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

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