Inequalities for the vibrating clamped plate problem
Yıl: 2001 Cilt: 25 Sayı: 2 Sayfa Aralığı: 283 - 298 Metin Dili: İngilizce İndeks Tarihi: 29-07-2022
Inequalities for the vibrating clamped plate problem
Öz: We study the eigenvalues of the vibrating clamped plate problem. We have made improvements on the bounds of the ratios of the eigenvalues of the biharmonic operator (clamped plate) using the methods of Payne, Polya, and Weinberger. The difference in our proof lies mainly with the trial functions and the orthogonality arguments. While Payne, Polya, and Weinberger and Hile and Yeh project away components along $u_1$,$u_2$,...,$u_k$ to meet the orthogonality conditions,we use a translation/rotation argument to meet these conditions.
Anahtar Kelime: Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık
- [1] G.N.Hile and R.Z.Yeh, Inequalities for eigenvalues of the biharmonic operator ", Pac.J.Math 112 (1984), 115-133.
- [2] S.M. Hook, Domain-independent upper bounds for eigenvalues of elliptic operators",Tran. AMer.Math.Soc. 318 (1990), 615-642.
- [3] L.E.Payne, G.Polya, and H.F.Weinberger, On the ratio of consecutive eigenvalues", J.Math.and Phys. 35 (1956), 289-298 [reprinted in G.Polya: Collected Papers, Vol. III:Analysis,J.Hersch and G.C.Rota, editors, MIT Press, Cambridge, Massachusetts, 1984, pp. 420-429,with comments by J.Hersch on pp. 521-522].
| APA | MCHALE K, UFUKTEPE U (2001). Inequalities for the vibrating clamped plate problem. , 283 - 298. |
| Chicago | MCHALE K.P.,UFUKTEPE U. Inequalities for the vibrating clamped plate problem. (2001): 283 - 298. |
| MLA | MCHALE K.P.,UFUKTEPE U. Inequalities for the vibrating clamped plate problem. , 2001, ss.283 - 298. |
| AMA | MCHALE K,UFUKTEPE U Inequalities for the vibrating clamped plate problem. . 2001; 283 - 298. |
| Vancouver | MCHALE K,UFUKTEPE U Inequalities for the vibrating clamped plate problem. . 2001; 283 - 298. |
| IEEE | MCHALE K,UFUKTEPE U "Inequalities for the vibrating clamped plate problem." , ss.283 - 298, 2001. |
| ISNAD | MCHALE, K.P. - UFUKTEPE, U.. "Inequalities for the vibrating clamped plate problem". (2001), 283-298. |
| APA | MCHALE K, UFUKTEPE U (2001). Inequalities for the vibrating clamped plate problem. Turkish Journal of Mathematics, 25(2), 283 - 298. |
| Chicago | MCHALE K.P.,UFUKTEPE U. Inequalities for the vibrating clamped plate problem. Turkish Journal of Mathematics 25, no.2 (2001): 283 - 298. |
| MLA | MCHALE K.P.,UFUKTEPE U. Inequalities for the vibrating clamped plate problem. Turkish Journal of Mathematics, vol.25, no.2, 2001, ss.283 - 298. |
| AMA | MCHALE K,UFUKTEPE U Inequalities for the vibrating clamped plate problem. Turkish Journal of Mathematics. 2001; 25(2): 283 - 298. |
| Vancouver | MCHALE K,UFUKTEPE U Inequalities for the vibrating clamped plate problem. Turkish Journal of Mathematics. 2001; 25(2): 283 - 298. |
| IEEE | MCHALE K,UFUKTEPE U "Inequalities for the vibrating clamped plate problem." Turkish Journal of Mathematics, 25, ss.283 - 298, 2001. |
| ISNAD | MCHALE, K.P. - UFUKTEPE, U.. "Inequalities for the vibrating clamped plate problem". Turkish Journal of Mathematics 25/2 (2001), 283-298. |
