Geodesic
Sobolev's embedding theorem for a domain with irregular boundary
Sbornik. Mathematics, Tome 192 (2001) no. 3, pp. 323-346

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In Sobolev's embedding theorem, $W_p^s(G)\subset L_q(G)$ the relations between admissible smoothness parameters and integrability parameters are determined by the geometric properties of the domain $G$. In the present paper this result and the corresponding estimates of weak type are established for domains with irregular boundaries and in the case of weighted $L_p$, $L_q$-spaces. 
@article{SM_2001_192_3_a0,
     author = {O. V. Besov},
     title = {Sobolev's embedding theorem for a domain with irregular boundary},
     journal = {Sbornik. Mathematics},
     pages = {323--346},
     publisher = {mathdoc},
     volume = {192},
     number = {3},
     year = {2001},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2001_192_3_a0/}
}
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O. V. Besov. Sobolev's embedding theorem for a domain with irregular boundary. Sbornik. Mathematics, Tome 192 (2001) no. 3, pp. 323-346. http://geodesic.mathdoc.fr/item/SM_2001_192_3_a0/