VARIATIONAL METHODS FOR INVERSE PROBLEMS

IAN KNOWLES

iwk@vorteb.math.uab.edu

Department of Mathematics

University of Alabama at Birmingham

University Station

Birmingham, AL 35294, USA

University of Alabama at Birmingham

University Station

Birmingham, AL 35294, USA

Inverse problems involving the recovery of coefficient functions in partial differential equations
from measurements involving the solutions,
are in general computationally difficult, verging on intractable. We consider recovery
methods based upon the
minimization of certain functionals with unique global minima and unique stationary points.
Applications include the electrical tomography problem, i.e.
the recovery of electrical conductivity from Dirichlet-Neumann map data, and
the full groundwater modelling problem.
The use of critical point theory in establishing uniqueness will also
be discussed.

EPSRC Gregynog Workshop, 21-26 July 2002