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THE KATO SQUARE ROOT PROBLEM FOR MIXED BOUNDARY VALUE PROBLEMS

Published online by Cambridge University Press:  18 August 2006

ANDREAS AXELSSON ,
STEPHEN KEITH  and
ALAN McINTOSH
ANDREAS AXELSSON
Affiliation:
Laboratoires de Mathématiques, Bât. 425, Université Paris-Sud, 91405 Orsay, Franceandreas.axelsson@math.u-psud.fr, kax74@yahoo.se
STEPHEN KEITH
Affiliation:
Centre for Mathematics and its Applications, Australian National University, Canberra, ACT 0200, Australiastephen.keith@anu.edu.au
ALAN McINTOSH
Affiliation:
Centre for Mathematics and its Applications, Australian National University, Canberra, ACT 0200, AustraliaAlan.McIntosh@maths.anu.edu.au
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Abstract

We solve the Kato square root problem for second order elliptic systems in divergence form under mixed boundary conditions on Lipschitz domains. This answers a question posed by Lions in 1962. To do this we develop a general theory of quadratic estimates and functional calculi for complex perturbations of Dirac-type operators on Lipschitz domains.

Keywords

35J2547B4447F05
Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 74 , Issue 1 , August 2006 , pp. 113 - 130
Copyright
The London Mathematical Society 2006

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