Quasi-conformal mappings and periodic spectral problems in dimension two

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dc.creatorShargorodsky, E.
dc.creatorSobolev, A. V.
dc.date2001-09-27
dc.date.accessioned2026-07-07T04:43:33Z
dc.date.available2026-07-07T04:43:33Z
dc.descriptionWe study spectral properties of second order elliptic operators with periodic coefficients in dimension two. These operators act in periodic simply-connected waveguides, with either Dirichlet, or Neumann, or the third boundary condition. The main result is the absolute continuity of the spectra of such operators. The corner stone of the proof is an isothermal change of variables, reducing the metric to a flat one and the waveguide to a straight strip. The main technical tool is the quasi-conformal variant of the Riemann mapping theorem.
dc.description36 pages
dc.identifierhttps://arxiv.org/abs/math/0109216
dc.identifierhttp://arxiv.org/abs/math/0109216
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/62273
dc.subjectSpectral Theory
dc.subject35J10, 30C20, 35J25
dc.titleQuasi-conformal mappings and periodic spectral problems in dimension two
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