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- W2949273309 abstract "We consider a family of domains $(Omega_N)_{N>0}$ obtained by attaching an $Ntimes 1$ rectangle to a fixed set $Omega_0 = {(x,y): 0<y<1, -phi(y)<x<0}$, for a Lipschitz function $phigeq 0$. We derive full asymptotic expansions, as $Ntoinfty$, for the $m$th Dirichlet eigenvalue (for any fixed $m$) and for the associated eigenfunction on $Omega_N$. The second term involves a scattering phase arising in the Dirichlet problem on the infinite domain $Omega_infty$. We determine the first variation of this scattering phase, with respect to $phi$, at $phiequiv 0$. This is then used to prove sharpness of results, obtained previously by the same authors, about the location of extrema and nodal line of eigenfunctions on convex domains." @default.
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- W2949273309 date "2007-10-19" @default.
- W2949273309 modified "2023-09-23" @default.
- W2949273309 title "Asymptotics of eigenfunctions on plane domains" @default.
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