The vanishing discount problem and viscosity Mather measures. Part 1: The problem on a torus

作者：Ishii Hitoshi^*; Mitake Hiroyoshi; Tran Hung V

来源：Journal de Mathematiques Pures et Appliquees, 2017, 108(2): 125-149.

DOI：10.1016/j.matpur.2016.10.013

• Ergodic problem
• Fully nonlinear
• Degenerate elliptic PDE
• Mather measures
• Vanishing discount

We develop a variational approach to the vanishing discount problem for fully nonlinear, degenerate elliptic, partial differential equations. Under mild assumptions, we introduce viscosity Mather measures for such partial differential equations, which are natural extensions of the Mather measures. Using the viscosity Mather measures, we prove that the whole family of solutions v(lambda) of the discount problem with the factor lambda > 0 converges to a solution of the ergodic problem as lambda -> 0.

• 出版日期2017-8