Harmonic Analysis and Partial Differential Equations

My research during the past five years can be divided into two main strands. The first is a long-standing interest, the study of boundary value problems for elliptic equations in non-smooth domains. My latest work on boundary value problems has focused on problems with mixed boundary conditions. A more recent area of investigation involves inverse boundary value problems and problems in scattering theory. The common element that binds these two different areas is an interest in using results from harmonic analysis to establish existence and uniqueness results under minimal hypotheses on the inputs to the problem. Here, inputs might mean the domain, the boundary data, or the coefficients of the operators.