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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
Affiliation:
Laboratoires de Mathématiques, Bât. 425, Université Paris-Sud, 91405 Orsay, [email protected], [email protected]
STEPHEN KEITH
Affiliation:
Centre for Mathematics and its Applications, Australian National University, Canberra, ACT 0200, [email protected]
ALAN McINTOSH
Affiliation:
Centre for Mathematics and its Applications, Australian National University, Canberra, ACT 0200, [email protected]
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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

Type
Notes and Papers
Copyright
The London Mathematical Society 2006

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