A Pogorelov-type counterexample to the discreteness and openness of gradient mappings

Deguang Zhong

Let $\Omega \subset {\mathbb{R}}^n$ be a domain, and suppose that $u\in W_{loc}^{2,n}(\Omega )$ satisfies the following ineqiality \[ \det D^2u\geq δ>0\qquad\text{a.e. in }Ω. \] A question of G…