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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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/
@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},
year = {1987},
volume = {163},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_1987_163_a1/}
}
TY - JOUR
AU - M. Sh. Birman
AU - M. Z. Solomyak
TI - Construction of a function of class $H^2$ with given conormal derivative in a piecewise smooth domain
JO - Zapiski Nauchnykh Seminarov POMI
PY - 1987
SP - 17
EP - 28
VL - 163
UR - http://geodesic.mathdoc.fr/item/ZNSL_1987_163_a1/
LA - ru
ID - ZNSL_1987_163_a1
ER -
%0 Journal Article
%A M. Sh. Birman
%A M. Z. Solomyak
%T Construction of a function of class $H^2$ with given conormal derivative in a piecewise smooth domain
%J Zapiski Nauchnykh Seminarov POMI
%D 1987
%P 17-28
%V 163
%U http://geodesic.mathdoc.fr/item/ZNSL_1987_163_a1/
%G ru
%F ZNSL_1987_163_a1
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 $m=3$.
