Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-27T06:17:57.306Z Has data issue: false hasContentIssue false

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]
Get access

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)