English

The Kato square root problem for mixed boundary value problems

Analysis of PDEs 2007-05-23 v2 Classical Analysis and ODEs

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.

Keywords

Cite

@article{arxiv.math/0412324,
  title  = {The Kato square root problem for mixed boundary value problems},
  author = {Andreas Axelsson and Stephen Keith and Alan McIntosh},
  journal= {arXiv preprint arXiv:math/0412324},
  year   = {2007}
}

Comments

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