Geodesic
Construction of a function of class $H^2$ with given conormal derivative in a piecewise smooth domain
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 19, Tome 163 (1987), pp. 17-28

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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 $m=3$. 
@article{ZNSL_1987_163_a1,
     author = {M. Sh. Birman and M. Z. Solomyak},
     title = {Construction of a function of class $H^2$ with given conormal derivative in a piecewise smooth domain},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {17--28},
     publisher = {mathdoc},
     volume = {163},
     year = {1987},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1987_163_a1/}
}
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M. Sh. Birman; M. Z. Solomyak. Construction of a function of class $H^2$ with given conormal derivative in a piecewise smooth domain. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 19, Tome 163 (1987), pp. 17-28. http://geodesic.mathdoc.fr/item/ZNSL_1987_163_a1/