Values of finite distortion: Reshetnyak's theorem, the Liouville theorem, and the Lusin (N) -property

Ilmari Kangasniemi, Jani Onninen, Yizhe Zhu

Let $\Omega \subset {\mathbb{R}}^n$ be a domain and $f\in W_{\text{loc}}^{1,n}(\Omega ,{\mathbb{R}}^n)$. We say that $f$ has a value of finite distortion at $y_0\in {\mathbb{R}}^n$ if there exist…