On the lower bound of the principal eigenvalue of a nonlinear operator
2021 ◽
Vol 61
(1)
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AbstractWe prove sharp lower bound estimates for the first nonzero eigenvalue of the non-linear elliptic diffusion operator $$L_p$$ L p on a smooth metric measure space, without boundary or with a convex boundary and Neumann boundary condition, satisfying $$BE(\kappa ,N)$$ B E ( κ , N ) for $$\kappa \ne 0$$ κ ≠ 0 . Our results extends the work of Koerber Valtorta (Calc Vari Partial Differ Equ. 57(2), 49 2018) for case $$\kappa =0$$ κ = 0 and Naber–Valtorta (Math Z 277(3–4):867–891, 2014) for the p-Laplacian.
2016 ◽
Vol 19
(01)
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pp. 1650001
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2010 ◽
Vol 17
(2)
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pp. 575-601
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2005 ◽
pp. 245-252
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