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2008 - 2009
announces
compact course on
The Square Root Problem of Kato for Elliptic Operators: Survey,
Solution and Sequel
by
Prof. Alan McIntosh
Centre for Mathematics and its Applications
Australian
National University
Canberra, Australia
November 03 - 07, 2008
at
L H – 1, Department of Mathematics
Indian Institute of Science, Bangalore
Abstract
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.
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