Partial Data Inverse Problems for Maxwell Equations via Carleman Estimates
نویسنده
چکیده
In this article we consider an inverse boundary value problem for the timeharmonic Maxwell equations. We show that the electromagnetic material parameters are determined by boundary measurements where part of the boundary data is measured on a possibly very small set. This is an extension of earlier scalar results of BukhgeimUhlmann and Kenig-Sjöstrand-Uhlmann to the Maxwell system. The main contribution is to show that the Carleman estimate approach to scalar partial data inverse problems introduced in those works can be carried over to the Maxwell system.
منابع مشابه
A Unified Controllability/Observability Theory for Some Stochastic and Deterministic Partial Differential Equations
The purpose of this paper is to present a universal approach to the study of controllability/observability problems for infinite dimensional systems governed by some stochastic/deterministic partial differential equations. The crucial analytic tool is a class of fundamental weighted identities for stochastic/deterministic partial differential operators, via which one can derive the desired glob...
متن کاملInverse problem for a parabolic system with two components by measurements of one component
We consider a 2×2 system of parabolic equations with first and zeroth coupling and establish a Carleman estimate by extra data of only one component without data of initial values. Then we apply the Carleman estimate to inverse problems of determining some or all of the coefficients by observations in an arbitrary subdomain over a time interval of only one component and data of two components a...
متن کاملAn Inverse Problem for Maxwell's Equations in Anisotropic Media an Inverse Problem for Maxwell's Equations in Anisotropic Media
We consider Maxwell’s equations for an isomagnetic anisotropic, non-stationary and inhomogeneous medium in two dimensions. We discuss an inverse problem of determining the permittivity tensor ε1 ε2 ε2 ε3 and the permeability μ in the constitutive relations from a finite number of lateral boundary measurements. Applying a Carleman estimate, we prove an estimate of the Lipschitz type for ...
متن کاملInverse Problems with Partial Data for a Dirac System: a Carleman Estimate Approach
We prove that the material parameters in a Dirac system with magnetic and electric potentials are uniquely determined by measurements made on a possibly small subset of the boundary. The proof is based on a combination of Carleman estimates for first and second order systems, and involves a reduction of the boundary measurements to the second order case. For this reduction a certain amount of d...
متن کاملCarleman Estimates and Inverse Problems for Dirac Operators
We consider limiting Carleman weights for Dirac operators and prove corresponding Carleman estimates. In particular, we show that harmonic functions can be considered as limiting Carleman weights for Dirac operators. As an application we consider the inverse problem of recovering a Lipschitz continuous magnetic field and electric potential from boundary measurements for the Pauli Dirac operator.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2015