Harmonic analysis and boundary value problems for elliptic systems

Harmonic analysis is the study of waves. Radio signals, sound waves, waves on a pond, can all be investigated in terms of their harmonic frequencies. Boundary value problems for partial differential equations arise naturally when physical problems are expressed in mathematical terms. This project concerns the systematic development of the harmonic analysis of partial differential operators in order to solve such problems on regions with irregular boundaries. Particular emphasis is given to studying elliptic systems such as the spatial component of Maxwell s equations for the propagation of electromagnetic waves.