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The Kato square root problem for mixed boundary value problems

Andreas Axelsson·Stephen Keith·Alan McIntosh
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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 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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Andreas Axelsson, Stephen Keith, Alan McIntosh. 2005-10-24. The Kato square root problem for mixed boundary value problems. https://arxiv.org/abs/math/0412324

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