7 papers
Regularity and non-degeneracy of implies regularity of the fixed boundary
Henrik Garde, Michael S. Vogelius
For a diffeomorphism of a domain onto itself, which is the identity on , we prove that local regularity of the push-forward implies local regul…
Limiting Absorption Principle and Radiation Condition for the Fractional Helmholtz Equation
Dana Zilberberg, Fioralba Cakoni, Michael S. Vogelius
We investigate elliptic fractional equations in the whole space, involving zero order perturbations of the fractional Laplacian , . Our main objective is to determi…
Transmission Eigenvalues and Non-scattering
Fioralba Cakoni, Michael S. Vogelius
In this paper we survey some recent results concerning scattering and non-scattering in the context of the linear Helmholtz equation and inhomogeneities of nontrivial contrast. We…
Scattering of plane waves
Narek Hovsepyan, Michael S. Vogelius
We formulate a problem that can be viewed as a natural variation of the so-called Pompeiu or Schiffer problem in the context of scattering of plane waves for the Linear Helmholtz e…
Scattering from analytic and piecewise analytic inhomogeneities
Narek Hovsepyan, Michael S. Vogelius
We study scattering for the linear Helmholtz operator in two dimensions and develop a technique, which can be used to ascertain scattering of a given incident wave from very regula…
Finiteness Results for Non-Scattering Herglotz Waves: The case of inhomogeneities obtained by very general perturbations of disks
Michael S. Vogelius, Jingni Xiao
We study non-scattering phenomena associated with the time-harmonic Helmholtz equation in two dimensions. For very general classes of star-shaped domains, we show that there are at…