14 citations · 50 across the 15 of their papers we have counts for
20 papers
Inverting the geodesic ray transform with finite measurements: stability and reconstruction
Yernat M. Assylbekov
We study the inversion of the geodesic ray transform from finitely many local averages of its data. Under suitable geometric assumptions, we prove Lipschitz stability on any fixed…
The attenuated ray transforms on Gaussian thermostats with negative curvature
Yernat M. Assylbekov, Franklin T. Rea
In the present paper we consider a Gaussian thermostat on a compact Riemannian surface with negative thermostat curvature. In the case of surfaces with boundary, we show that the t…
Unique recovery of electrical conductivity and magnetic permeability from Magneto-Telluric data
Yernat M. Assylbekov, Maarten V. de Hoop
We present a comprehensive mathematical study of the Magneto-Telluric (MT) method, on bounded domain in . We show that electrical conductivity and magnetic permeabili…
Inverse problems for nonlinear Maxwell's equations with second harmonic generation
Yernat Assylbekov, Ting Zhou
In the current paper we consider an inverse boundary value problem of electromagnetism with nonlinear Second Harmonic Generation (SHG) process. We show the unique determination of…
The attenuated geodesic ray transform on tensors: generic injectivity and stability
Yernat M. Assylbekov
We consider the attenuated geodesic ray transform defined on pairs of symmetric -tensors and -forms on a simple Riemannian manifold. We prove injectivity and stability result…
A sharp stability estimate for the geodesic ray transform
Yernat Assylbekov, Plamen Stefanov
We prove a sharp stability estimate for the geodesic X-ray transform of tensor fields of order , and on a simple Riemannian manifold with a suitable cho…
Direct and inverse problems for the nonlinear time-harmonic Maxwell equations in Kerr-type media
Yernat M. Assylbekov, Ting Zhou
In the current paper we consider an inverse boundary value problem of electromagnetism in a nonlinear Kerr medium. We show the unique determination of the electromagnetic material…
Determining rough first order perturbations of the polyharmonic operator
Yernat M. Assylbekov, Karthik Iyer
We show that the knowledge of Dirichlet to Neumann map for rough and in for for a bounded domain in , determines $…
A note on time-harmonic Maxwell equations on Riemannian manifolds
Yernat M. Assylbekov
In this note we consider boundary value problems in electromagnetism. We prove well-posedness results for the time-harmonic Maxwell equations in the setting of Riemannian manifolds…
Inversion formulas and range characterizations for the attenuated geodesic ray transform
Yernat Assylbekov, François Monard, Gunther Uhlmann
We present two range characterizations for the attenuated geodesic X-ray transform defined on pairs of functions and one-forms on simple surfaces. Such characterizations are based…
Reconstruction in the partial data Calderón problem on admissible manifolds
Yernat M Assylbekov
We consider the problem of developing a method to reconstruct a potential from the partial data Dirichlet-to-Neumann map for the Schrödinger equation on a fixed a…
Inverse problems for the perturbed polyharmonic operator with coefficients in Sobolev spaces with non-positive order
Yernat M. Assylbekov
We show that the knowledge of the Dirichlet-to-Neumann map on the boundary of a bounded open set in , , for the perturbed polyharmonic operator $(-Δ)^m+A\cdot…
Determining the first order perturbation of a polyharmonic operator on admissible manifolds
Yernat M. Assylbekov, Yang Yang
We consider the inverse boundary value problem for the first order perturbation of the polyharmonic operator , with being a vector field and…
Invariant distributions and tensor tomography for Gaussian thermostats
Yernat M. Assylbekov, Hanming Zhou
In this paper we consider the Gaussian thermostat ray transform on both closed Riemannian surfaces and compact Riemannian surfaces with boundary. We establish certain results on th…
On the range of the attenuated magnetic ray transform for connections and Higgs fields
Gareth Ainsworth, Yernat M. Assylbekov
For a two-dimensional simple magnetic system, we study the attenuated magnetic ray transform , with attenuation given by a unitary connection and a skew-Hermitian Higg…
An inverse radiative transfer in refractive media equipped with a magnetic field
Yernat M. Assylbekov, Yang Yang
We study the reconstruction of the attenuation and absorption coefficients in a stationary linear transport equation from knowledge of albedo operator in dimension on a R…
Boundary and scattering rigidity problems in the presence of a magnetic field and a potential
Yernat M. Assylbekov, Hanming Zhou
In this paper, we consider a compact Riemannian manifold with boundary, endowed with a magnetic potential and a potential . For brevity, this type of systems are called $\MP…
Attenuated tensor tomography on simple surfaces
Yernat M. Assylbekov
In this paper we consider the geodesic X-ray transform with attenuation coefficient as a combination of smooth complex function and 1-form. We show that attenuated X-ray transform…
The X-ray transform on a general family of curves on Finsler surfaces
Yernat M. Assylbekov, Nurlan S. Dairbekov
We consider a general family of curves on a compact oriented Finsler surface with boundary . Let and a smooth 1-form on . We sho…
Hopf type rigidity for thermostats
Yernat M. Assylbekov, Nurlan S. Dairbekov
We show a Hopf type rigidity for thermostats without conjugate points on a 2-torus