This paper gives a result for the existence of a minimizer for an energy functional of the kind \(\int_\Omega g(\nabla u(x))dx\), where \(g\) is nonnegative and is zero only on potential wells described by rotations of finitely many matrices \(A_1,\dots,A_r\). The problem of finding a minimizer is than equivalent to solving the differential inclusion \[ \nabla u(x)\in\bigcup^r_{i=1} \text{SO}(3)A_i, \] where \(\text{SO}(3)\) describe rotations of matrices \(A_i\). In the paper, it is proved that for any open and bounded set \(\Omega\subset\mathbb{R}^3\) the problem \[ \nabla u(x)\in \text{SO}(3)I\cup \text{SO}(3)I^-,\quad|u|_{\partial\Omega}= 0, \] where \[ I^-=\begin{pmatrix} -1 & 0 & 0\\ 0 & 1 & 0\\ 0 & 0 & 1\end{pmatrix} \] has a solution.