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
In arXiv:1603.01051 (Part 1 of this series), we have introduced a variational approach to studying the vanishing discount problem for fully nonlinear, degenerate elliptic, partial differential equations in a torus. We develop this approach further here to handle boundar... View more
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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