On a quadratic estimate related to the Kato conjecture and boundary value problems
By P. Auscher, A. Axelsson, A. Mcintosh. 2008
88 citations recorded by the source corpus.
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.
Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/cd98703ffab3dc874b1c31eda491386fd5b0fbc8
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In Applied Mathematics
- P. Auscher
- A. Axelsson
- A. Mcintosh
- S. Hofmann
- Svitlana Mayboroda
- J. M. Martell
- Dachun Yang
- Mihalis Mourgoglou
In Computational Theory and Mathematics
In Mathematical Physics
- P. Auscher
- A. Axelsson
- A. Mcintosh
- S. Hofmann
- J. M. Martell
- Svitlana Mayboroda
- Mihalis Mourgoglou
- Tuomas Hytönen
Citations in the corpus
- Solvability of elliptic systems with square integrable boundary data (2008, background): “se it was proved in [10, Theorem 3.1(iii)], building on results for the Kato problem by Auscher, Hofmann, Lacey, McIntosh and Tchamitchian [5]. It is also possible to give a direct proof, as shown in [4]. Theorem 3.4. Let Dbe a self-adjoint homogeneous first order differential operator with constant c”
- Weighted maximal regularity estimates and solvability of non-smooth elliptic systems I (2009, methodology): “Our methods build on an algebraic reduction to a first order system first made for coefficients A0 by the two authors and A. McIntosh in order to use functional calculus related to the Kato conjecture solution, and the main analytic tool for coefficients A is an operational calculus to prove weighte”