PDE Seminar Abstracts

First order techniques in the solution of second order boundary value problems

Alan McIntosh
Australian National University
22 August 2011 2-3pm, Eastern Avenue Seminar Room 405


The first order Cauchy Riemann equations have long been used in the study of harmonic boundary value problems in the plane. The Dirac operator can sometimes be employed in higher dimensions. Perturbed Dirac operators provided insight into the solution of the Kato square-root problem for elliptic operators. In recent joint work with Andreas Axelsson and Pascal Auscher, we show how they can also be used to study the solvability of elliptic equations with square integrable boundary conditions. I shall survey this chain of ideas.