Geodesic
On Rellich's inequalities in the Euclidean spaces
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2018), pp. 83-87

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On domains of the Euclidean spaces we consider inequalities for test functions and their Laplacians. We describe a family of domains having vanishing Rellich constants. For the Euclidean space of dimension 4 we present a new version of the Rellich inequality. In addition we prove new one-dimensional Rellich-type integral inequalities for linear combinations of test functions and their derivatives of orders one and two.
Keywords: Laplace operator, Rellich inequality, uniformly perfect set, real spherical harmonics, Hardy inequality. 
@article{IVM_2018_8_a9,
     author = {F. G. Avkhadiev},
     title = {On {Rellich's} inequalities in the {Euclidean} spaces},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {83--87},
     publisher = {mathdoc},
     number = {8},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2018_8_a9/}
}
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F. G. Avkhadiev. On Rellich's inequalities in the Euclidean spaces. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2018), pp. 83-87. http://geodesic.mathdoc.fr/item/IVM_2018_8_a9/