Recovery of an unknown support of a source term in an elliptic equation
Abstract
In this paper, we consider the inverse problem of determining the shape and location of inhomogeneity D in an elliptic equation with a Neumann boundary condition \frac{\partial u}{\partial \nu} = g on partOHgr \vphantom{\frac{1}{2}}\!\Delta u(x) + p \chi_D(x)u(x) = 0, \qquad x \in \Omega,
where \overline{D} \subset \Omega and khgr_{D} is the characteristic function of a subdomain D. We discuss the global uniqueness in determining D by a single measurement of Dirichlet data u on partOHgr and prove uniqueness results with extra information on domains D.
 Publication:

Inverse Problems
 Pub Date:
 April 2004
 DOI:
 10.1088/02665611/20/2/016
 Bibcode:
 2004InvPr..20..565K
 Keywords:

 inverse problemuniquenessunknown support