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

Yucheng Tu

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

Analysis of PDEs 2021-10-08 v2

Authors: Yucheng Tu

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 $\kappa\neq 0$ . Our results extends the work of Koerber[5] for case $\kappa=0$ and Naber-Valtorta[10] for the $p$ -Laplacian.

Keywords

principal eigenvalue nonlinear operator elliptic diffusion smooth metric measure space neumann boundary lower bound

Cite

@article{arxiv.2008.00185,
  title  = {On the Lower Bound of the Principal Eigenvalue of a Nonlinear Operator},
  author = {Yucheng Tu},
  journal= {arXiv preprint arXiv:2008.00185},
  year   = {2021}
}

Related papers

View all related →