Comparison estimates on the first eigenvalue of a quasilinear elliptic system
Keyword(s):
AbstractWe study a system of quasilinear eigenvalue problems with Dirichlet boundary conditions on complete compact Riemannian manifolds. In particular, Cheng comparison estimates and the inequality of Faber–Krahn for the first eigenvalue of a {(p,q)}-Laplacian are recovered. Lastly, we reprove a Cheeger-type estimate for the p-Laplacian, {1<p<\infty}, from where a lower bound estimate in terms of Cheeger’s constant for the first eigenvalue of a {(p,q)}-Laplacian is built. As a corollary, the first eigenvalue converges to Cheeger’s constant as {p,q\to 1,1}.
2009 ◽
Vol 11
(01)
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pp. 59-69
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2001 ◽
Vol 64
(3)
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pp. 381-393
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2015 ◽
Vol 422
(1)
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pp. 1-26
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2005 ◽
Vol 2005
(13)
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pp. 2005-2010
2018 ◽
Vol 265
(9)
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pp. 4133-4157
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