Construction of a function of class $H^2$ with given conormal derivative in a piecewise smooth domain

Let $\Omega\subset\mathbb{R}^m$ be a domain with Lipshitz boundary. She article is devoted to the problem of construction of function $\Phi\in H^2(\Omega)$ whose conormal derivative on $\partial\Omega$ coincides with the normal component of a given vector field $u\in H^1(\Omega,\mathbb{C}^3)$.We give solution of this problem for piecewise smooth boundary and $m=3$.