Geodesic
A Remark on the Steklov--Poincar\'e Inequality
Matematičeskie zametki, Tome 110 (2021) no. 2, pp. 234-238.

Voir la notice de l'article provenant de la source Math-Net.Ru

In an $n$-dimensional bounded domain $\Omega_n$, $n\ge 2$, we prove the Steklov–Poincaré inequality with the best constant in the case where $\Omega_n$ is an $n$-dimensional ball. We also consider the case of an unbounded domain with finite measure, in which the Steklov–Poincaré inequality is proved on the basis of a Sobolev inequality.
Keywords: Steklov's inequality, Poincaré inequality, Sobolev inequality
Mots-clés : best constant. 
@article{MZM_2021_110_2_a5,
     author = {Sh. M. Nasibov},
     title = {A {Remark} on the {Steklov--Poincar\'e} {Inequality}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {234--238},
     publisher = {mathdoc},
     volume = {110},
     number = {2},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2021_110_2_a5/}
}
TY  - JOUR
AU  - Sh. M. Nasibov
TI  - A Remark on the Steklov--Poincar\'e Inequality
JO  - Matematičeskie zametki
PY  - 2021
SP  - 234
EP  - 238
VL  - 110
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2021_110_2_a5/
LA  - ru
ID  - MZM_2021_110_2_a5
ER  - 
%0 Journal Article
%A Sh. M. Nasibov
%T A Remark on the Steklov--Poincar\'e Inequality
%J Matematičeskie zametki
%D 2021
%P 234-238
%V 110
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2021_110_2_a5/
%G ru
%F MZM_2021_110_2_a5
Sh. M. Nasibov. A Remark on the Steklov--Poincar\'e Inequality. Matematičeskie zametki, Tome 110 (2021) no. 2, pp. 234-238. http://geodesic.mathdoc.fr/item/MZM_2021_110_2_a5/

[1] B. C. Vladimirov, Uravneniya matematicheskoi fiziki, Nauka, M., 1981 | MR

[2] E. Krahn, Über Minimaleigenschaften der Kugel in drei und mehr Dimensionen, Acta Comm. Univ. Tartu. (Dorpat), A9, Göttingen, 1926

[3] G. Faber, “Beweis, dass unter allen homogenen Membranen von gleicher Fläche und gleicher Spannung die kreisförmige den tiefsten Grundton gibt”, Sitzungsber. Bayrischen Akad. Wiss München, Math.-Phys. KL, 1923, 169–172 | Zbl

[4] E. Krahn, “Über eine von Rayleigh formulierte Minimal eigenschaft des Kreises”, Math. Ann., 94 (1925), 97–100 | DOI | MR | Zbl

[5] J. W. S. Rayleigh, The Theory of Sound, Macmillan, London, 1894/96 | MR

[6] W. Stekloff, “Remarque complémentaire au Mémoire: “Sur les expressions asymptotiques de certaines fonctions, définies par les équations différentielles etc.””, Soobsch. Kharkov. matem. obsch. Vtoraya ser., 10 (1907), 200 | Zbl

[7] B. C. Vladimirov, I. I. Markush, Vladimir Andreevich Steklov – uchenyi i organizator nauki, Nauka, M., 1981 | MR

[8] Sh. M. Nasibov, “Ob optimalnykh konstantakh v nekotorykh neravenstvakh Soboleva i ikh prilozhenii k nelineinomu uravneniyu Shredingera”, Dokl. AN SSSR, 307:3 (1989), 538–542

[9] Sh. M. Nasibov, “Interpolyatsionnoe neravenstvo Soboleva i logarifmicheskoe neravenstvo Grossa–Soboleva”, Matem. zametki, 107:6 (2020), 894–901 | DOI | MR | Zbl

[10] I. S. Gradshtein, I. M. Ryzhik, Tablitsy integralov, summ, ryadov i proizvedenii, Nauka, M., 1971 | MR