Geodesic
Hardy Inequality with a Singular Weight inside a Domain
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 154 (2012) no. 3, pp. 173-179

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We consider Sobolev spaces with singular weights at some internal points of a 2D-domain. For the functions of these spaces, Hardy inequality is proved. Embedding theorems for weighted Sobolev spaces and theorems on equivalent renorming are obtained.
Keywords: Hardy inequality, weighted Sobolev spaces, embedding theorems, equivalent renorming theorems. 
@article{UZKU_2012_154_3_a15,
     author = {M. R. Timerbaev and N. V. Timerbaeva},
     title = {Hardy {Inequality} with {a~Singular} {Weight} inside {a~Domain}},
     journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
     pages = {173--179},
     publisher = {mathdoc},
     volume = {154},
     number = {3},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/UZKU_2012_154_3_a15/}
}
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M. R. Timerbaev; N. V. Timerbaeva. Hardy Inequality with a Singular Weight inside a Domain. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 154 (2012) no. 3, pp. 173-179. http://geodesic.mathdoc.fr/item/UZKU_2012_154_3_a15/