دانشگاه شهید باهنر کرمان

 آمار

تعداد نشریات26
تعداد شماره‌ها447
تعداد مقالات4,557
تعداد مشاهده مقاله5,379,993
تعداد دریافت فایل اصل مقاله3,580,059
Azami, Shahroud, Zohrehvand, Mosayeb, Fasihi-Ramandi, Ghodratallah. (1403). Some inequalities for eigenvalues of an elliptic differential operator. , 14(1), 137-154. doi: 10.22103/jmmr.2024.22939.1582
Shahroud Azami; Mosayeb Zohrehvand; Ghodratallah Fasihi-Ramandi. "Some inequalities for eigenvalues of an elliptic differential operator". , 14, 1, 1403, 137-154. doi: 10.22103/jmmr.2024.22939.1582
Azami, Shahroud, Zohrehvand, Mosayeb, Fasihi-Ramandi, Ghodratallah. (1403). 'Some inequalities for eigenvalues of an elliptic differential operator', , 14(1), pp. 137-154. doi: 10.22103/jmmr.2024.22939.1582
Azami, Shahroud, Zohrehvand, Mosayeb, Fasihi-Ramandi, Ghodratallah. Some inequalities for eigenvalues of an elliptic differential operator. , 1403; 14(1): 137-154. doi: 10.22103/jmmr.2024.22939.1582

Some inequalities for eigenvalues of an elliptic differential operator

Journal of Mahani Mathematical Research
دوره 14، شماره 1 - شماره پیاپی 31، فروردین 2025، صفحه 137-154    اصل مقاله (493.17 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22103/jmmr.2024.22939.1582
نویسندگان
Shahroud Azami1؛ Mosayeb Zohrehvand2؛ Ghodratallah Fasihi-Ramandi* 1
1Department of Pure Mathematics, Imam Khomeini International University, Qazvin, Iran.
2Department of mathematics, Malayer University, Malayer, Iran
چکیده
‎In the present paper, we investigate  the eigenvalues of an elliptic differential operator on compact Riemannian manifolds with boundary and derive a general inequality for these eigenvalues. Applying this inequality, we give universal estimates  for eigenvalues on compact domains of  complete submanifolds in an Euclidean space, and of complete manifolds admitting special functions. Finally, we find universal bounds on  the $(k+1)$-th eigenvalue on such objects in terms of the first $k$ eigenvalues independent of  the domains.
کلیدواژه‌ها
Universal bound‎؛ ‎Elliptic operator‎؛ ‎Eigenvalue‎؛ ‎submanifold
مراجع
[1] Ashbaugh M., (2002), The universal eigenvalue bounds of Payne-Polya-Weinberger, Hile{Protter, and H C Yang, Proc. Indian Acad. Sci. (Math. Sci.) 112(1), 3-30. https://doi.org/10.1007/BF02829638

[2] Ballmann W., Gromov M., & Schroeder V., (1985), Manifolds of nonpositive curvature, 273, Birkhauser, Boston. https://doi.org/10.1007/978-1-4684-9159-3

[3] Chen D., Cheng Q. M., (2008), Extrinsic estimates for eigenvalues of the Laplace operator, J. Math. Soc. Jpn., 60, 325-339. https://doi.org/10.2969/jmsj/06020325

[4] Cheng Q. M., Yang H. C., (2006), Inequalities for eigenvalues of a clamped plate problem, Trans. Amer. Math. Soc. 358 (6), 2625-2635. https://doi.org/10.1090/S0002-9947-05-04023-7

[5] do Carmo M. P., Wang Q., Xia C., (2010), Inequalities for eigenvalues of elliptic operators in divergence form on Riemannian manifolds, Annali di mathematica, 189, 643-660. https://doi.org/10.1007/s10231-010-0129-2

[6] Harrell E. M., (2007), Commutators, eigenvalue gaps and mean curvature in the theory of Schrodinger operators, Commun. Partial Di er. Equ., 32, 401-413. https://doi.org/10.1080/03605300500532889

[7] Harrell E. M., El Sou  A., & Ilias A., (2009), Universal inequalities for the eigenvalues of Laplace and Schrodinger operator on submanifolds, Trans. Amer. Math. Soc., 361(5), 2337-2350. https://doi.org/10.1090/S0002-9947-08-04780-6

[8] Heintz E., Im Hof H. C., (1977), Geometry of horospheres, J. Di . Geom., 12, 481-489. https://doi.org/10.4310/jdg/1214434219

[9] Hile G. N., Yeh R. Z., (1984), Inequalities for eigenvalues of the biharmonic operator, Paci c J. math., 112, 115-133.

[10] Jost J, .t, Jost X. L., Wang Q., & Xia C., (2011), Universal bounds for eigenvalues of the polyharmonic operators, Trans. Amer. Math. Soc., 363(4), 1821-1854. https://doi.org/10.1090/S0002-9947-2010-05147-5

[11] Li P., (1980) Eigenvalue estimates on homogeneouse manifolds, Comment. Math. Helv., 55, 347-363. https://doi.org/10.1007/BF02566692

[12] Payn L. E., Polya G., & Weinberger H. F., On the ratio of consecutive eigenvalues, J. Math. and Phys., 35, 289-298. https://doi.org/10.1002/sapm1956351289

[13] Sakai T., (1956), On Reimannian manifolds admitting a function whose gradient is of constant norm, Kodai Math. J., 19(1996),39-51. https://doi.org/10.2996/kmj/1138043545

[14] Sei pour D., (2022), On the spectral geometry of 4-dimensional Lorentzian Lie group, J. of Finsler Geom. Appl. 3(2), 99-118. https://doi.org/10.22098/jfga.2022.11917.1080

[15] Wang Q., Xia C., (2011), Inequalities for eigenvalues of a clamped plate problem, Cal. Var. PDE., 40, 273-289. https://doi.org/10.1007/s00526-010-0340-4

[16] Yang H. C., (1991), An estimate of the di erence between consecutive eigenvalues, Preprint IC/91/60 of ICTP, Trieste.

آمار
تعداد مشاهده مقاله: 153
تعداد دریافت فایل اصل مقاله: 166


سامانه مدیریت نشریات علمی. طراحی و پیاده سازی از سیناوب