publication . Preprint . Article . 2016

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

Hitoshi Ishii; Hiroyoshi Mitake; Hung V. Tran;
Open Access English
  • Published: 16 Jul 2016
Abstract
Comment: 40 pages
Subjects
free text keywords: Mathematics - Analysis of PDEs, 35B40, 35J70, 49L25, Degenerate energy levels, Partial differential equation, Boundary value problem, Torus, Dirichlet problem, Nonlinear system, Mathematics, Convergence (routing), Neumann boundary condition, Mathematical analysis
21 references, page 1 of 2

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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publication . Preprint . Article . 2016

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

Hitoshi Ishii; Hiroyoshi Mitake; Hung V. Tran;