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Asymptotics of the principal eigenvalue of an elliptic operator on closed and orientable Riemannian manifolds: small diffusion
Xin Xu, Kexin Zhang
This paper is concerned with the asymptotic behavior of the principal eigenvalue of the elliptic eigenvalue problem \[ -DΔ_{M}u - a\langle \nabla_M f, \nabla_M u\rangle_g +…
Asymptotics of the principal eigenvalue of an elliptic operator on closed and orientable Riemannian manifolds
Xin Xu, Kexin Zhang
This paper investigates the asymptotic behavior of the principal eigenvalue , as , for the following elliptic eigenvalue problem \begin{equation*}\label{E} -Δ_{M…
Non-convergence of the principal eigenvalue of elliptic operators for large advection
Xueli Bai, Zhi-An Wang, Xin Xu +2
This paper investigates the limit of the principal eigenvalue as for the following elliptic equation \begin{align*} -Δφ(x)-2s\mathbf{v}\cdot\nablaφ(x)+c(x)φ(x)…
A Counterexample for the Principal Eigenvalue of An Elliptic Operator with Large Advection
Xueli Bai, Xin Xu, Kexin Zhang +1
There are numerous studies focusing on the convergence of the principal eigenvalue as corresponding to the elliptic eigenvalue problem \begin{align*} -Δφ(x)-2s…