Abstract
We study spectral properties of elliptic problems of order 2m with periodic coefficients in L ∞. Our goal is to obtain a Floquet-Bloch type representation of the spectrum in terms of the spectra of associated operators acting on the period cell. Our approach using bilinear forms and operators in H -m-type spaces easily handles discontinuous coefficients and has the merit of being rather direct. In addition, the cell of periodicity is allowed to be unbounded, i.e., periodicity is not required in all spatial directions.
Mathematics Subject Classification (2000). 35J10, 35j30, 35J99, 35P10.
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Brown, B.M., Hoang, V., Plum, M., Wood, I.G. (2011). Floquet-Bloch Theory for Elliptic Problems with Discontinuous Coefficients. In: Janas, J., Kurasov, P., Laptev, A., Naboko, S., Stolz, G. (eds) Spectral Theory and Analysis. Operator Theory: Advances and Applications(), vol 214. Springer, Basel. https://doi.org/10.1007/978-3-7643-9994-8_1
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