Differential Inclusions Involving the Curl Operator

In this article, we study the existence of $\eta \in W_0^{1,\mathrm{\infty }}(\mathrm{\Omega };{\mathbb{R}}^n)$ satisfying $$\text{curl }\eta \in E\text{ a.e. in }\mathrm{\Omega },$$ where $n\in \mathbb{N},\mathrm{\Omega }\subseteq {\mathbb{R}}^n$ is open, bounded and $E\subseteq {\mathrm{\Lambda }}^2\mathrm{.}$