TY - JOUR AU - Hencl, Stanislav PY - 2010/12/01 Y2 - 2024/03/29 TI - On the weak differentiability of $u\circ f^{-1}$ JF - MATHEMATICA SCANDINAVICA JA - Math. Scand. VL - 107 IS - 2 SE - Articles DO - 10.7146/math.scand.a-15151 UR - https://www.mscand.dk/article/view/15151 SP - 198-208 AB - Let $p\geq n-1$ and suppose that $f:\Omega\to{\mathsf R}^n$ is a homeomorphism in the Sobolev space $W^{1,p}_{(\mathrm{loc}}(\Omega,{\mathsf R}^n)$. Further let $u\in W^{1,q}_{(\mathrm{loc}}(\Omega)$ where $q=\frac{p}{p-(n-1)}$ and for $q>n$ we also assume that $u$ is continuous. Then $u\circ f^{-1}\in (\mathrm{BV}_{(\mathrm{loc}}(f(\Omega))$ and if we moreover assume that $f$ is a mapping of finite distortion, then $u\circ f^{-1}\in W^{1,1}_{(\mathrm{loc}}(f(\Omega))$. ER -