Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On a quadratic estimate related to the Kato conjecture and boundary
  value problems   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.

23
The categories of this paper are: solv-int
0
The categories of this paper are: hep-ph
15
The categories of this paper are: nucl-ex
7
The categories of this paper are: hep-th
27
The categories of this paper are: comp-gas
36
The categories of this paper are: cmp-lg
4
The categories of this paper are: cond-mat
26
The categories of this paper are: bayes-an
9
The categories of this paper are: nlin
8
The categories of this paper are: hep-ex
18
The categories of this paper are: econ
5
The categories of this paper are: gr-qc
12
The categories of this paper are: nucl-th
3
The categories of this paper are: physics
6
The categories of this paper are: astro-ph
32
The categories of this paper are: atom-ph