Speaker

:

Prof. Alan McIntosh

Australian National University Canberra, Australia

Subject Area

:

Mathematics

Venue

:

Lecture Hall - I, Dept of Mathematics

Time

:

4.00 pm

Date  

:

Nov 3 - 7,2008 (Monday to Friday)

Title

:

The Square Root Problem of Kato for Elliptic Operators:Survey,Solution and Sequel

About 1960 Tosio Kato, during his investigation of the evolution of physical systems, was led to pose a key question about the square root of non-symmetric elliptic partial differential operators in divergence form. The one-dimensional problem was solved by Coifman, Meyer and myself in 1982, while it was only in 2001 that the question was fully answered by Auscher, Hofmann, Lacey, Tchamitchian and myself. A more general viewpoint was subsequently provided in joint work of mine with Axelsson and Keith.

Recently, these ideas were employed to give conditions for the solvability of non-symmetric elliptic partial differential equations with bounded measurable coefficients and square integrable boundary values. I shall survey these applications of harmonic analysis to the study of elliptic pde's, and present a new approach of Auscher, Axelsson and myself.