Geodesic
Sobolev Embedding Theorems for a~Class of Anisotropic Irregular Domains
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Function theory and nonlinear partial differential equations, Tome 260 (2008), pp. 297-319

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Sufficient conditions for the embedding of a Sobolev space in Lebesgue spaces on a domain depend on the integrability and smoothness parameters of the spaces and on the geometric features of the domain. In the present paper, Sobolev embedding theorems are obtained for a class of domains with irregular boundary; this class includes the well-known classes of $\sigma$-John domains, domains with the flexible cone condition, and their anisotropic analogs. 
@article{TM_2008_260_a19,
     author = {Boris V. Trushin},
     title = {Sobolev {Embedding} {Theorems} for {a~Class} of {Anisotropic} {Irregular} {Domains}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {297--319},
     publisher = {mathdoc},
     volume = {260},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2008_260_a19/}
}
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Boris V. Trushin. Sobolev Embedding Theorems for a~Class of Anisotropic Irregular Domains. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Function theory and nonlinear partial differential equations, Tome 260 (2008), pp. 297-319. http://geodesic.mathdoc.fr/item/TM_2008_260_a19/