Abstract
Let \(\Omega \) be a bounded domain in a n-dimensional Euclidean space \(\mathbb {R}^{n}\). We study eigenvalues of an eigenvalue problem of a system of elliptic equations of the drifting Laplacian
Estimates for eigenvalues of the above eigenvalue problem are obtained. Furthermore, a universal inequality for lower order eigenvalues of the problem is also derived. Finally, we prove an universal inequality type Ashbaugh and Benguria for the drifting Laplacian on Riemannian manifold immersed in an unit sphere or a projective space.
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The authors are very grateful to the referee for the valuable suggestions which lead to improvements in the manuscript.
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Communicated by A. Jüngel.
Rosane Gomes Pereira supported in part by CAPES/REUNI. Levi Adriano supported by CAPES/PNPD and FAPEG.
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Pereira, R.G., Adriano, L. & Cavalheiro, A. Universal inequalities for eigenvalues of a system of elliptic equations of the drifting Laplacian. Monatsh Math 181, 797–820 (2016). https://doi.org/10.1007/s00605-015-0875-8
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DOI: https://doi.org/10.1007/s00605-015-0875-8