Selection problems for a discount degenerate viscous Hamilton-Jacobi equation

作者：Mitake Hiroyoshi; Tran Hung V^*

来源：Advances in Mathematics, 2017, 306: 684-703.

DOI：10.1016/j.aim.2016.10.032

• Selection problem
• Degenerate viscous Hamilton-Jacobi equations
• Ergodic problems
• Nonlinear adjoint methods

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 using the nonlinear adjoint method and deriving a commutation lemma. This convergence result was first proven by Davini, Fathi, Iturriaga, and Zavidovique for first order Hamilton Jacobi equations.

• 出版日期2017-1-14