Distribution of resonances for the Neumann problem in linear elasticity outside a strictly convex body

DOI10.1215/S0012-7094-95-07825-9zbMath0846.35139MaRDI QIDQ1902024

Plamen D. Stefanov, Georgi Vodev

Publication date: 6 October 1996

Published in: Duke Mathematical Journal (Search for Journal in Brave)

zbMATH Keywords

Neumann boundary conditionsresonancesexterior problemelasticity operator

Mathematics Subject Classification ID

Classical linear elasticity (74B05) Second-order elliptic equations (35J15)

Related Items

Rayleigh and Stoneley waves in linear elasticity, Sharp High-Frequency Estimates for the Helmholtz Equation and Applications to Boundary Integral Equations, Neumann resonances in linear elasticity for an arbitrary body, Applying GMRES to the Helmholtz equation with strong trapping: how does the number of iterations depend on the frequency?, Wavenumber-Explicit Parametric Holomorphy of Helmholtz Solutions in the Context of Uncertainty Quantification, Resolvent estimates in strips for obstacle scattering in 2D and local energy decay for the wave equation, Fractal Weyl law for open quantum chaotic maps, Approximation of the elastic Dirichlet-to-Neumann map, Quasimodes and resonances: sharp lower bounds, Asymptotic behaviour of the scattering phase in linear elasticity for a strictly convex body, Construction of Rayleigh quasimodes with a large life time, Transmission eigenvalue-free regions, The transmission problem in linear isotropic elasticity, Pseudospectra of semiclassical (pseudo-) differential operators, Distribution of Resonances in Scattering by Thin Barriers, Unnamed Item, Resonance projectors and asymptotics for 𝑟-normally hyperbolic trapped sets, Eigenvalues of the Truncated Helmholtz Solution Operator under Strong Trapping, Unnamed Item

Cites Work

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• Scattering frequencies and Gevrey 3 singularities
• Precise informations on the poles of the scattering matrix for two strictly convex obstacles
• Sharp bounds on the number of scattering poles for perturbations of the Laplacian
• On the local-energy decay property for the elastic wave equation with the Neumann boundary condition
• Microlocal parametrices for diffractive boundary value problems
• Diffraction by a convex obstacle
• Trapping obstacles with a sequence of poles on the scattering matrix converging to the real axis
• The complex scaling method for scattering by strictly convex obstacles
• On the poles of the scattering matrix for two strictly convex obstacles
• A logarithmic bound on the location of the poles of the scattering matrix
• Singularities of boundary value problems. II
• Decaying and nondecaying properties of the local energy of an elastic wave outside an obstacle
• Existence and uniqueness of a rayleigh surface wave propagating along the free boundary of a transversely isotropic elastic half space
• Rayleigh Quasimodes In Linear Elasticity
• Singularities of boundary value problems. I
• Oscillatory integrals, lagrange immersions and unfolding of singularities