The limiting absorption principle for the two-dimensional inhomogeneous anisotropic elasticity system

Unique Continuation for the Two-dimensional Anisotropic Elasticity System and Its Applications to Inverse Problems

Under some generic assumptions we prove the unique continuation property for the two-dimensional inhomogeneous anisotropic elasticity system. Having established the unique continuation property, we then investigate the inverse problem of reconstructing the inclusion or cavity embedded in a plane elastic body with inhomogeneous anisotropic medium by infinitely many localized boundary measurements.

The Limiting Absorption Principle for a Periodic Semi-Infinite Waveguide

We study an elliptic boundary value problem in a semi-infinite, straight waveguide containing a periodic material distribution. The spectral parameter is taken to lie in a spectral band of the corresponding full-space periodic operator. In contrast to the situation with constant coefficients, it is not obvious how to define the “outgoing” solution of the problem. In order to define the outgoing...

Limiting absorption principle for the dissipative Helmholtz equation

This equation modelizes accurately the propagation of the electromagnetic field of a laser in material medium. Here k0 is the wave number of the laser in the vacuum, N and a are smooth nonnegative functions representing the electronic density of material medium and the absorption coefficient of the laser energy by material medium, and A0 is an incident known excitation (see [BLSS03]). Note that...

A Limiting Absorption Principle for the three-dimensional Schrödinger equation with L potentials

(1) sup λ>λ0, ε>0 ∥−4 + V − (λ + iε) )−1∥∥ L2,σ(Rd)→L2,−σ(Rd) <∞ provided that λ0 > 0, (1 + |x|)1+|V (x)| ∈ L∞ and σ > 12 . Here L(R) = {(1 + |x|)−σ f : f ∈ L(R)} is the usual weighted L2. The bound (1) is obtained from the same estimate for V = 0 by means of the resolvent identity. This bound for the free resolvent is related to the so called trace lemma, which refers to the statement that for...

Inhomogeneous anisotropic percolation: Two-dimensional numerical threshold analysis.