HIGH FREQUENCY LIMIT OF THE HELMHOLTZ EQUATION. II. SOURCE ON A GENERAL SMOOTH MANIFOLD

DOI10.1081/PDE-120002867zbMath1290.35262WikidataQ60502918 ScholiaQ60502918MaRDI QIDQ4547610

Perthame, Benoît, Olof Runborg, Francois Castella

Publication date: 2002

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Mathematics Subject Classification ID

PDEs in connection with optics and electromagnetic theory (35Q60) PDEs in connection with quantum mechanics (35Q40) Elliptic equations on manifolds, general theory (58J05) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42A38) Perturbations in context of PDEs (35B20) PDEs in connection with mechanics of deformable solids (35Q74) Equilibrium (steady-state) problems in solid mechanics (74G99)

Related Items (11)

Besov estimates in the high-frequency Helmholtz equation, for a non-trapping and \(C^{2}\) potential ⋮ Mathematical models for laser-plasma interaction ⋮ High frequency limit of Helmholtz equations: refraction by sharp interfaces ⋮ Semiclassical measure for the solution of the dissipative Helmholtz equation ⋮ High frequency limit for a chain of harmonic oscillators with a point Langevin thermostat ⋮ High-Frequency Limit of the Inverse Scattering Problem: Asymptotic Convergence from Inverse Helmholtz to Inverse Liouville ⋮ High frequency limit of the Helmholtz equations. ⋮ The radiation condition at infinity for the high-frequency Helmholtz equation with source term: a wave-packet approach ⋮ Limit measures for the Helmholtz equation in the non-trapping case ⋮ Uniform resolvent estimates for a non-dissipative Helmholtz equation ⋮ High-frequency limit of the Helmholtz equation with variable refraction index

Cites Work

• Asymptotic properties of solutions of differential equations with simple characteristics
• Morrey-Campanato estimates for Helmholtz equations
• On Wigner measures
• Ergodic properties of eigenfunctions for the Dirichlet problem
• H-measures, a new approach for studying homogenisation, oscillations and concentration effects in partial differential equations
• Microlocal defect measures
• Homogenization limits and Wigner transforms
• On the Quantum Correction For Thermodynamic Equilibrium

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