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.
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