On the Lower Bound of the Principal Eigenvalue of a Nonlinear Operator

Yucheng Tu

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arXiv · 2008.00185

On the Lower Bound of the Principal Eigenvalue of a Nonlinear Operator

Yucheng Tu

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Abstract

We prove sharp lower bound estimates for the first nonzero eigenvalue of the non-linear elliptic diffusion operator $L_p$ on a smooth metric measure space, without boundary or with a convex boundary and Neumann boundary condition, satisfying $BE(κ,N)$ for $κ\neq 0$. Our results extends the work of Koerber[5] for case $κ=0$ and Naber-Valtorta[10] for the $p$-Laplacian.

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Yucheng Tu. 2021-10-07. On the Lower Bound of the Principal Eigenvalue of a Nonlinear Operator. https://arxiv.org/abs/2008.00185

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