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The vanishing discount problem for fully nonlinear degenerate elliptic PDEs

Banff International Research Station for Mathematical Innovation and Discovery

I explain an approach, based on generalized Mather measures, to the vanishing discount problem for fully nonlinear, degenerate elliptic, partial differential equations. Under mild assumptions, we introduce viscosity Mather measures for such PDEs, which are natural extensions of Mather measures, originally due to J. Mather. Using the viscosity Mather measures, one can show that the whole family of solutions $v^\lambda$ of the discounted problem, with the discount factor $\lambda$, converges to a solution of the ergodic problem as $\lambda$ goes to 0. This is based on joint work with Hiroyoshi Mitake (Hiroshima University) and Hung V. Tran (University of Wisconsin, Madison).

Mathematics; Partial differential equations; Integral equations

video/mp4

Author affiliation: Waseda University

2017-10-01

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/63158

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/