Spectral gaps in the Dirichlet problem for the biharmonic operator on a plane periodically perforated by circular holes

DOI10.3103/S1063454113020039zbMath1285.35118OpenAlexW2061334264MaRDI QIDQ2439842

Fedor L. Bakharev

Publication date: 17 March 2014

Published in: Vestnik St. Petersburg University. Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3103/s1063454113020039

zbMATH Keywords

Dirichlet problemasymptotic analysisbiharmonic operatorspectral gapsperiodic waveguide

Mathematics Subject Classification ID

General topics in linear spectral theory for PDEs (35P05) Plates (74K20) PDEs in connection with mechanics of deformable solids (35Q74) Boundary value problems for higher-order elliptic systems (35J58)

Related Items (1)

Localization of eigenfunctions in a narrow Kirchhoff plate

Cites Work

• Gaps in the spectrum of the Neumann problem on a perforated plane
• Spectral gaps in the Dirichlet and Neumann problems on the plane perforated by a doubleperiodic family of circular holes
• Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I
• Essential spectrum of a periodic elastic waveguide may contain arbitrarily many gaps
• Floquet theory for partial differential equations

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