Spectral Anomalies of the Robin Laplacian in Non-Lipschitz Domains
С. А. Назаров, Jari Taskinen · Institutional Repositories DataBase (IRDB) · 2013
We consider the spectral Laplace-Robin problem in bounded peak shaped domains of Rn, n ≥ 2. In case of a sufficiently sharp peak and ”wrong” sign of the Robin coefficients, the spectrum becomes pathological: the residual spectrum covers the whole complex plane, while all complex numbers are eigenvalues of the adjoint problem operator. Our results solve a spectral problem posed by H. Amann and D. Daners.