On a quadratic estimate related to the Kato conjecture and boundary value problems

@article{Auscher2010OnAQ,
  title={On a quadratic estimate related to the Kato conjecture and boundary value problems},
  author={P. Auscher and A. Axelsson and A. McIntosh},
  journal={arXiv: Classical Analysis and ODEs},
  year={2010},
  volume={505}
}
  • P. Auscher, A. Axelsson, A. McIntosh
  • Published 2010
  • Mathematics
  • arXiv: Classical Analysis and ODEs
  • We provide a direct proof of a quadratic estimate that plays a central role in the determination of domains of square roots of elliptic operators and, as shown more recently, in some boundary value problems with $L^2$ boundary data. We develop the application to the Kato conjecture and to a Neumann problem. This quadratic estimate enjoys some equivalent forms in various settings. This gives new results in the functional calculus of Dirac type operators on forms. 
    68 Citations
    The Kato Square Root Problem on Vector Bundles with Generalised Bounded Geometry
    • 12
    • PDF
    Geometry and the Kato square root problem
    • 1
    • PDF
    Boundary value problems for degenerate elliptic equations and systems
    • 11
    • PDF
    Rough metrics on manifolds and quadratic estimates
    • 9
    • PDF
    Elliptic Boundary Value Problems With Fractional Regularity Data: The First Order Approach
    • 4
    • PDF
    $L^2$ well-posedness of boundary value problems for parabolic systems with measurable coefficients
    • 7
    • PDF
    Weighted maximal regularity estimates and solvability of non-smooth elliptic systems I
    • 66
    • PDF
    Holomorphic functional calculus of Hodge-Dirac operators in Lp
    • 13
    • Highly Influenced
    • PDF

    References

    SHOWING 1-10 OF 31 REFERENCES
    The Kato Square Root Problem for Mixed Boundary Value Problems
    • 62
    • PDF
    Quadratic estimates and functional calculi of perturbed Dirac operators
    • 109
    • PDF
    The solution of the Kato square root problem for second order elliptic operators on Rn
    • 280
    • PDF
    The regularity and Neumann problem for non-symmetric elliptic operators
    • 25
    • Highly Influential
    • PDF
    The neumann problem for elliptic equations with non-smooth coefficients
    • 108