Related papers: Linearized internal functionals for anisotropic co…
We consider a semilinear elliptic equation in a bounded domain with zero boundary conditions. The nonlinearity is discontinuous and monotone, but it is not a Carath\'eodory's function. The existence theorem has been proved.
This article is dedicated to the anisotropic sparse grid quadrature for functions which are analytically extendable into an anisotropic tensor product domain. Taking into account this anisotropy, we end up with a dimension independent error…
We consider inverse problems estimating distributed parameters from indirect noisy observations through discretization of continuum models described by partial differential or integral equations. It is well understood that the errors…
We provide a mathematical analysis and a numerical framework for magnetoacoustic tomography with magnetic induction. The imaging problem is to reconstruct the conductivity distribution of biological tissue from measurements of the Lorentz…
In this paper, we study the equilibria of an anisotropic, nonlocal aggregation equation with nonlinear diffusion which does not possess a gradient flow structure. Here, the anisotropy is induced by an underlying tensor field. Anisotropic…
We study the existence and uniqueness for weak solutions to some classes of anisotropic elliptic Dirichlet problems with data belonging to the natural dual space.
Electrical and elasticity imaging are promising modalities for a suite of different applications including medical tomography, non-destructive testing, and structural health monitoring. These emerging modalities are capable of providing…
We consider the inverse problem of recovering an isotropic electrical conductivity from interior knowledge of the magnitude of one current density field generated by applying current on a set of electrodes. The required interior data can be…
We predict theoretically and demonstrate experimentally an ellipticity-dependent nonlinear magneto-optic rotation of elliptically-polarized light propagating in a coherent atomic medium. We show that this effect results from a hexadecapole…
Consider an inverse problem of the simultaneous recovery of boundary impedance and internal conductivity in the electrical impedance tomography (EIT) model using local internal measurement data, which is governed by a boundary value problem…
In the late 1950's, Eshelby's linear solutions for the deformation field inside an ellipsoidal inclusion and, subsequently, the infinite matrix in which it is embedded were published. The solutions' ability to capture the behavior of an…
In part I we introduced modified Landweber-Kaczmarz methods and have established a convergence analysis. In the present work we investigate three applications: an inverse problem related to thermoacoustic tomography, a nonlinear inverse…
In this article, we study an inverse problem with local data for a linear polyharmonic operator with several lower order tensorial perturbations. We consider our domain to have an inaccessible portion of the boundary where neither the input…
This paper considers the iterative solution of linear systems arising from discretization of the anisotropic radiative transfer equation with discontinuous elements on the sphere. In order to achieve robust convergence behavior in the…
We prove uniqueness and stability for an inverse boundary problem associated to an anisotropic elliptic equation arising in the modeling of prestressed elastic membranes.
For icosahedral inflation, we compute the tensor modes' two-point function in the presence of higher derivative corrections, and show that in general this features anisotropies that are aligned with the underlying icosahedral structure. The…
We introduce a framework for the reconstruction and representation of functions in a setting where these objects cannot be directly observed, but only indirect and noisy measurements are available, namely an inverse problem setting. The…
The purpose of this paper is to propose a non-iterative method for the inverse conductivity problem of recovering multiple small anomalies from the boundary measurements. When small anomalies are buried in a conducting object, the electric…
Given a conformally transversally anisotropic manifold $(M,g)$, we consider the semilinear elliptic equation $$(-\Delta_{g}+V)u+qu^2=0\quad \text{on $M$}.$$ We show that an a priori unknown smooth function $q$ can be uniquely determined…
We present a counterexample concerning the monotone discretization of elliptic problems with mixed derivatives on anisotropic meshes.