Compact Courses
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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