# Sharp estimates of the generalized principal eigenvalue for superlinear viscous Hamilton-Jacobi equations with inward drift

## TL;DR

This paper derives precise estimates for the generalized principal eigenvalue of superlinear viscous Hamilton-Jacobi equations with inward drift and vanishing potential at infinity, under radial symmetry assumptions.

## Contribution

It provides sharp bounds for the eigenvalue considering perturbations of the potential in equations with inward drift and superlinear Hamiltonian.

## Key findings

- Established sharp estimates of the eigenvalue
- Analyzed the effect of potential perturbations
- Focused on equations with inward-pointing drift

## Abstract

This paper is concerned with the ergodic problem for viscous Hamilton-Jacobi equations having superlinear Hamiltonian, inward-pointing drift, and positive potential which vanishes at infinity. Assuming some radial symmetry of the drift and the potential outside a ball, we establish sharp estimates of the generalized principal eigenvalue with respect to a perturbation of the potential.