Critical Sobolev thresholds for openness and discreteness of Monge-Ampere gradient mappings

Deguang Zhong

Let $\Omega \subset {\mathbb{R}}^n$ be a domain and let $u\in W^{2,n}_{\loc}(Ω)$ satisfy \[ \det D^2u\geqδ>0\qquad\text{a.e. in }Ω. \] Guerra and Tione asked whether the gradient mapping $Du$ must…