3 problems

Let ${\Bbb D}$ be the unit disk, and let $f_0:\overline{{\Bbb D}}\to\overline{{\Bbb D}}$ be a homeomorphism of finite distortion with … Here ${\cal A}:[1,\infty)\to[1,\infty)$ is c…

Let $\Omega\subset \mathbb R^n$ be a bounded open connected domain with $n\geq 3$. Let $u\in W^{1,n}(\Omega)$ and $v\in W^{1,1}(\Omega)$ satisfy … almost everywhere, and suppose th…

Let $\Omega\subset\mathbb{R}^n$ be a domain, let $f\in W^{1,n}_{\operatorname{loc}}(\Omega,\mathbb{R}^n)$, and let $K_I(\cdot,f)$ denote the inner distortion of $f$. Assume that…