3 citations · 3 across the 9 of their papers we have counts for
5 papers · 1 filter
Scattering of plane waves and a modified Pompeiu criterion
Narek Hovsepyan, Michael S. Vogelius
In this paper we prove that plane waves always scatter from bounded, strictly convex planar inhomogeneities with constant material parameters. Our approach involves the introductio…
On the potential lack of response in a model of second-harmonic generation. A computer-assisted proof
Miguel Ayala, Dominic Blanco, Fioralba Cakoni +2
This paper provides a rigorous computer-assisted proof of the existence of generalized transmission eigenvalues arising in nonlinear optics in the context of high-order harmonic ge…
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 determin…
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…