پیوندهای مفید
آمار
| تعداد نشریات | 21 |
| تعداد شماره‌ها | 610 |
| تعداد مقالات | 9,028 |
| تعداد مشاهده مقاله | 67,082,839 |
| تعداد دریافت فایل اصل مقاله | 7,656,342 |
Bounds to the first eigenvalues of weighted p-Steklov and (p,q)-Laplacian Steklov problems | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 26، دوره 14، شماره 7، مهر 2023، صفحه 295-307 اصل مقاله (384.55 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2022.27506.3630 | ||
| نویسنده | ||
| Shahroud Azami* | ||
| Department of Pure Mathematics, Faculty of Sciences, Imam Khomeini International University, Qazvin, Iran | ||
| تاریخ دریافت: 25 خرداد 1401، تاریخ پذیرش: 01 آبان 1401 | ||
| چکیده | ||
| We consider the Steklov problem associated with the weighted p-Laplace operator and $(p,q)$-Laplacian on submanifolds with the boundary of Euclidean spaces and prove Reilly-type upper bounds for their first eigenvalues. | ||
| کلیدواژه‌ها | ||
| Steklov problem؛ Eigenvalue؛ hypersurfaces | ||
| مراجع | ||
|
[1] H. Alencar, M.P. Carmo and H. Rosenberg, On the first eigenvalue of linearized operator of the r-th mean curvature of a hypersurface, Ann. Glob. Anal. Geom. 11 (1993), 387–395. [2] L.J. Alias and J.M. Malacarne, On the first eigenvalue of the linearized operator of the higher order mean curvature for closed hypersurfaces in space forms, Illinois J. Math. 48 (2004), no. 1, 219–240. [3] J.L.M. Barbosa and A.G. Colares, Stability of hypersurfaces with constant r-mean curvature, Ann. Global Anal. Geom. 15 (1997), 277–297. [4] L. Barbu and G. Morosanu, On a Steklov eigenvalue problem associated with the (p, q)-Laplacian, Carpathian J. Math. 37 (2021), no. 2, 161–171. [5] L. Barbu and G. Morosanu, Eigenvalue of the negative (p, q)-Laplacian under a Steklov-like boundary condition, Complex Var. Elliptic Equ. 64 (2019), no. 4, 685–700. [6] L. Barbu and G. Morosanu, Full Description of the eigenvalue set of the (p, q)-Laplacian with a Steklov-like boundary condition, J. Differ. Equ. 290 (2021), 1–16. [7] M. Batista, M.P. Cavalcante and J. Pyo, Some isomperimetric inequalities and eigenvalue estimate in weighted manifolds, J. Math. Anal. Appl. 419 (2014), no. 1, 617–626. [8] M. C. Domingo-Juan and V. Miquel, Reilly’s type inequality for the Laplacian associated to a density related with shrinkers for MCF, arXiv: 1503.01332. [9] F. Du and J. Mao, Reilly-type inequalities for the p-Laplacian on compact Riemannian manifolds, Front. Math. China 10 (2015), no. 3, 583–594. [10] F. Du, J. Mao, Q. Waang and C. Xia, Estimates for eigenvalues of weighted Laplacian and weighted p-Laplacian, Hiroshima Math. J. 51 (2021), 225–253. [11] J.F. Grosjean, Upper bounds for the first eigenvalue of the Laplacian on compact manifolds, Pac. J. Math. 206 (2002), no. 1, 93–111. [12] R. C. Reilly, On the first eigenvalue of the Laplacian for compact submanifolds of Euclidean space, Comment. Math. Helv. 52 (1977), 525–533. [13] J. Roth, Upper bonds for the first eigenvalue of the Laplacian in terms of anisiotropic mean curvatures, Results Math. 64 (2013), no. 3-4, 383–403. [14] J. Roth, General Reilly-type inequalities for submanifolds of weighted Euclidean spaces, Colloq. Math. 144 (2016), no. 1, 127–136. [15] J. Roth, Reilly-type inequalities for Paneitz and Steklov eigenvalues, Potential Anal. 53 (2020), 773–798. [16] J. Roth, Extrinsic upper bounds the first eigenvalue of the p-Steklov problem on submanifolds, Commun. Math. 30 (2022), no. 1, 49–61. [17] H.J. Sun, C. Han and L. Zeng, Lower bounds for the first eigenvalues of the p-Laplacian and the weighted p-Laplacian, Math. Inequal. Appl. 23 (2020), no. 2, 585–596. [18] L.F. Wang, Eigenvalue estimate for the weighted p-Laplacian, Ann. Mat. 191 (2012), 539–550. [19] Y.Z. Wang and H.Q. Li, Lower bound estimates for the first eigenvalue of the weighted p-Laplacian on smooth metric measure spaces, Diff. Geom. Appl. 45 (2016), 23–42. | ||
|
آمار تعداد مشاهده مقاله: 16,352 تعداد دریافت فایل اصل مقاله: 170 |
||