The Kato square root problem for mixed boundary value problems

Andreas Axelsson; Stephen Keith; Alan McIntosh

doi:10.1112/S0024610706022873

The Kato square root problem for mixed boundary value problems

Andreas Axelsson^*, Stephen Keith, Alan McIntosh

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

54 Citations (Scopus)

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.

Original language	English
Pages (from-to)	113-130
Number of pages	18
Journal	Journal of the London Mathematical Society
Volume	74
Issue number	1
DOIs	https://doi.org/10.1112/S0024610706022873
Publication status	Published - Aug 2006

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title = "The Kato square root problem for mixed boundary value problems",

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.",

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AB - 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.

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The Kato square root problem for mixed boundary value problems

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