The Kato square root problem for mixed boundary value problems
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.
To appear in the Journal of the London Mathematical Society. This arxiv version is distinct from the final version