The Kato square root problem for mixed boundary value problems

2004/12/16 by Axelsson, Andreas, Keith, Stephen, McIntosh, Alan
#35J25 #47B44 #47F05 #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.math/0412324

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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