Our research interests are primarily in the fields of the Calculus of Variations and in integral equation methods in Mathematical Physics, specifically in applications to problems in acoustics, electromagnetics, and hydromechanics.

In the Calculus of Variations we have studied problems of optimal control for systems governed by functional differential equations and integral equations, including issues related to “deparameterized” problems involving differential and integral equations with set-valued mappings. Recently, we have initiated investigations of control problems defined on “infinite horizons” which often arise in models of economic systems and of problems in which optimal trajectories may well be discontinuous, but of bounded variation.

We have also worked in the application of integral equation methods to a variety of problems in acoustic and electromagnetic scattering, including integral representations of solutions of the Helmholtz and Maxwell equations , and the optimal design of radiating structures (antennas). In this latter context, we have studied new methods of multicriteria optimization as applied to conflicting physical constraints often present in antenna technology. Recently, we have started the study of direct and inverse problems of acoustic scattering in waveguides. Currently, much of this work is supported by the Air Force Office of Scientific Research under a MURI grant.