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

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 $BE(\kappa ,N)$ for $\kappa \ne 0$. Our results extends the work of Koerber[5] for case $\kappa =0$ and Naber-Valtorta[10] for the $p$-Laplacian.

References in corpus (4)

• Sharp estimate on the first eigenvalue of the p-Laplacian on compact manifold with nonnegative Ricci curvature
• Sharp estimates on the first eigenvalue of the p-Laplacian with negative Ricci lower bound
• Sharp lower bound for the first eigenvalue of the Weighted $p$-Laplacian
• Sharp Estimates for the Principal Eigenvalue of the p-Operator

Cited by in corpus (1)

• On a class of quasilinear operators on smooth metric measure spaces