Vanishing discount problem and the additive eigenvalues on changing domains

Limit of solutions for semilinear Hamilton-Jacobi equations with degenerate viscosity

“…Their approach relies on a dynamical characterization of the Mather measures in light of the weak KAM theory. Following the same approach, other convergence problems were gradually considered in [1,6,20,28]. Recently, the convergence of viscosity solution was proved in [30] for (HJ λ e ) with α(x) ≡ 0 (as λ → 0 + ), under Tonelli assumptions on H(x, p, u).…”

Global semiconcavity of solutions to first-order Hamilton-Jacobi equations with state constraints

“…It starts with [21] in the settings of optimal control theory, followed by further results like [5,10,11]. The asymptotic behavior of solutions to (1) in various settings can be found in [12,13,15,24]. For local semiconcavity of Hamilton-Jacobi equations with state constraints, see [3,20].…”