Nazarov, Sergey A.; Taskinen, Jari On essential and continuous spectra of the linearized water-wave problem in a finite pond. (English) Zbl 1191.35016 Math. Scand. 106, No. 1, 141-160 (2010). The authors show that the spectrum of the Laplace equation with the Steklov spectral boundary condition, in the connection of the linearized theory of water-waves, can have a nontrivial essential component even in case of a bounded basin with a horizontal water surface. The appearance of the essential spectrum is caused by the boundary irregularities of the type of a rotational cusp or a cuspidal edge. In a previous paper the authors have proven a similar result for the Steklov spectral problem in a bounded domain with a sharp peak. Reviewer: Titus Petrila (Cluj-Napoca) Cited in 10 Documents MSC: 35A18 Wave front sets in context of PDEs 37A30 Ergodic theorems, spectral theory, Markov operators 76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction 35P05 General topics in linear spectral theory for PDEs Keywords:Steklov spectral boundary condition; boundary irregularities; rotational cusp; cuspidal edge PDFBibTeX XMLCite \textit{S. A. Nazarov} and \textit{J. Taskinen}, Math. Scand. 106, No. 1, 141--160 (2010; Zbl 1191.35016) Full Text: DOI