Geodesic
The~Boundary Behavior of Functions of Sobolev Spaces Defined on a~Planar Domain with a~Peak Vertex on the~Boundary
Matematičeskie trudy, Tome 6 (2003) no. 1, pp. 3-27.

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Let $G$ be a domain with piecewise smooth boundary $\partial G$ and with vertices of exterior peaks on the boundary and let $k$ functions $f_1,\dots,f_k$ ($k$ is a nonnegative integer) be given on $\partial G$. We find necessary and sufficient conditions for existence of a function $F\in W_p^l(G)$, where $1$ and $l\geqslant k+1$ is an integer, such that $\frac{\partial^r F}{\partial N^r} \bigr\vert_{\partial G}=f_r$, $r=0,1,\dots,k$, with $N$ a unit vector field defined on $\partial G$ and nontangent to $\partial G$. 
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     author = {M. Yu. Vasil'chik},
     title = {The~Boundary {Behavior} of {Functions} of {Sobolev} {Spaces} {Defined} on {a~Planar} {Domain} with {a~Peak} {Vertex} on {the~Boundary}},
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M. Yu. Vasil'chik. The~Boundary Behavior of Functions of Sobolev Spaces Defined on a~Planar Domain with a~Peak Vertex on the~Boundary. Matematičeskie trudy, Tome 6 (2003) no. 1, pp. 3-27. http://geodesic.mathdoc.fr/item/MT_2003_6_1_a0/

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