## The vanishing discount problem and viscosity Mather measures. Part 2: boundary value problems

*Ishii, Hitoshi*;

*Mitake, Hiroyoshi*;

*Tran, Hung V.*;

- Subject: Mathematics - Analysis of PDEs | 35B40, 35J70, 49L25

- References (21)
The set GS(z, λ)′ is indeed the dual cone of GS(z, λ) in RL. Set PS := PΩ×A, and, for any compact subset K of A, let PKS denote the subset of all probability measures μ ∈ PS that have support in Tn × K, that is, and, hence, that u is a subsolution of (3.11), with θ = 1. Next, we consider the case when t ≥ 1. By (3.4) and (3.12), we get λvλ(z) ≥ lim hμ1k, Li + λhμ02, gi = ρ + hμ01, Li + λhμ02, gi, k→∞

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