The Kato square root problem for mixed boundary value problems

Details The Kato square root problem for mixed boundary value problems The Kato square root problem for mixed boundary value problems

2004-12-16

arxiv.org/abs/math/0412324v2

Mathematics

Analysis of PDEs

To appear in the Journal of the London Mathematical Society. This arxiv version is distinct from the final version

Scientific paper

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.

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