Geodesic
Rellich inequalities for polyharmonic operators in plane domains
Sbornik. Mathematics, Tome 209 (2018) no. 3, pp. 292-319

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Functionals whose values are defined as sharp constants in Rellich inequalities are investigated for polyharmonic operators in plane domains. The weight function is taken to be a power of the distance of a point to the boundary of the domain. Estimates are obtained for arbitrary domains, as is a test for these constants to be positive, and precise values are found for convex domains and for domains close to convex in a certain sense. The case when the weight function is taken to be a power of the coefficient in the Poincaré metric is also treated. Bibliography: 28 titles.
Keywords: Rellich inequality, polyharmonic operator, uniformly perfect set, Poincaré metric. 
@article{SM_2018_209_3_a1,
     author = {F. G. Avkhadiev},
     title = {Rellich inequalities for polyharmonic operators in plane domains},
     journal = {Sbornik. Mathematics},
     pages = {292--319},
     publisher = {mathdoc},
     volume = {209},
     number = {3},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2018_209_3_a1/}
}
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F. G. Avkhadiev. Rellich inequalities for polyharmonic operators in plane domains. Sbornik. Mathematics, Tome 209 (2018) no. 3, pp. 292-319. http://geodesic.mathdoc.fr/item/SM_2018_209_3_a1/