Selection problems for a discounted degenerate viscous Hamilton--Jacobi equation
Analysis of PDEs
2014-08-14 v1
Abstract
We prove that the solution of the discounted approximation of a degenerate viscous Hamilton--Jacobi equation with convex Hamiltonians converges to that of the associated ergodic problem. We characterize the limit in terms of stochastic Mather measures by naturally using the nonlinear adjoint method, and deriving a commutation lemma. This convergence result was first achieved by Davini, Fathi, Iturriaga, and Zavidovique for the first order Hamilton--Jacobi equation.
Cite
@article{arxiv.1408.2909,
title = {Selection problems for a discounted degenerate viscous Hamilton--Jacobi equation},
author = {Hiroyoshi Mitake and Hung V. Tran},
journal= {arXiv preprint arXiv:1408.2909},
year = {2014}
}