On essential and continuous spectra of the linearized water-wave problem in a finite pond

• Autores: Sergey A. Nazarov, Jari Taskinen
• Localización: Mathematica scandinavica, ISSN 0025-5521, Vol. 106, Nº 1, 2010, págs. 141-160
• Idioma: inglés
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• Resumen

  • We 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.