5 problems

Higher-dimensional openness and discreteness conjecture. In higher dimensions, every non-constant mapping $f\in W^{1,n}_{\mathrm{loc}}(\Omega,\mathbb{R}^n)$ of finite distortion wi…

p-Douglas conjecture. If $cvarphi$ satisfies the $p$-Douglas condition, then $cvarphi$ admits a $cmathscr{W}^{1,p}$-homeomorphic extension to $cmathbb{D}$.

Homeomorphism conjecture. Every minimizer $h_\circ\in\mathscr M^p(\overline{\mathbb{X}},\overline{\mathbb{Y}})$ is a homeomorphism.

The paper considers homeomorphisms and several distributional versions of the adjugate of the gradient matrix, including the conditions used to characterize bounded-variation regul…

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…