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 
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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     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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Voir la notice de l'article provenant de la source Math-Net.Ru

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 $\partial G$.

[1] Besov O. V., Ilin V. P., Nikolskii S. M., Integralnye predstavleniya funktsii i teoremy vlozheniya, Nauka, M., 1975 | MR | Zbl

[2] Vasilchik M. Yu., “O neobkhodimykh i dostatochnykh usloviyakh na sled funktsii iz prostranstva Soboleva na granitse ploskoi oblasti s nelipshitsevoi granitsei”, Issledovaniya po matematicheskomu analizu i rimanovoi geometrii, Nauka, Novosibirsk, 1992, 5–29 | MR

[3] Vasilchik M. Yu., “Granichnye svoistva funktsii iz prostranstva Soboleva, opredelennykh v ploskoi oblasti s uglovymi tochkami”, Sib. mat. zhurn., 36:4 (1995), 787–804 | MR | Zbl

[4] Vasilchik M. Yu., “Obratimaya kharakteristika sledov funktsii iz prostranstva Soboleva na kusochno-gladkoi granitse ploskoi oblasti”, Prostranstva Soboleva i smezhnye voprosy analiza, Nauka, Novosibirsk, 1996, 40–57 | MR

[5] Vilenkin N. Ya., Kombinatorika, Nauka, M., 1969 | MR | Zbl

[6] Grisvard P., Elliptic Problems in Nonsmooth Domains, Monographs and Studies in Mathematics, 24, Pitman, Boston; London, 1985 | MR | Zbl