Asymptotics of eigenfunctions on plane domains

Daniel Grieser, David Jerison

We consider a family of domains $({\Omega }_N{)}_{N>0}$ obtained by attaching an $N\times 1$ rectangle to a fixed set ${\Omega }_0=\{(x,y):0<y<1,-\varphi (y)<x<0\}$, for a Lipschitz function $\varphi \ge 0$.…