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arXiv:math/0412324 [math.AP]AbstractReferencesReviewsResources

The Kato square root problem for mixed boundary value problems

Andreas Axelsson, Stephen Keith, Alan McIntosh

Published 2004-12-16, updated 2005-10-24Version 2

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 J.-L. 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.

Comments: To appear in the Journal of the London Mathematical Society. This arxiv version is distinct from the final version
Categories: math.AP, math.CA
Subjects: 35J25, 47B44, 47F05
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