Vanishing discount problem and the additive eigenvalues on changing domains

Son N. T. Tu

We study the asymptotic behavior, as $\lambda \to 0^{+}$, of the state-constraint Hamilton--Jacobi equation $\varphi (\lambda )u_{\lambda }(x)+H(x,D{u}_{\lambda }(x))=0$ in $(1+r(\lambda ))\Omega$ and the corresponding add…