The Cosserat spectrum, named after the Cosserat brothers, authors of the notes C. R. Acad. Sc. (Paris), (1898): 126 1089-1091 and 127 315-318, is the set of real sigma such that the operator
with boundary conditions of Dirichlet or Neumann type, is not invertible.
We review results by Friedrichs (1937), Mikhlin (1973), Horgan and Payne (1983), Stoyan (1996), Crouzeix (1997), concerning the localization of the discrete and essential spectra.
We prove a new characterization of the essential spectrum in a polygonal domain.
We present an asymptotic analysis for thin rectangles (when the aspect ratio tends to zero) and show how these result may extrapolate to the case of a square.
Slides of a conference given in EPFL (Lausanne, Switzerland) in January 2000.
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PDF file (212 k) 16 January 2000. |
