Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Hardy constant of non-convex planar domains: the case of the
  quadrilateral   The Hardy constant of a simply connected domain $\Omega\subset\R^2$ is the
best constant for the inequality \[ \int_{\Omega}|\nabla u|^2dx \geq
c\int_{\Omega} \frac{u^2}{{\rm dist}(x,\partial\Omega)^2}\, dx \;, u\in
C^{\infty}_c(\Omega). \] After the work of Ancona where the universal lower
bound 1/16 was obtained, there has been a substantial interest on computing or
estimating the Hardy constant of planar domains. In this work we determine the
Hardy constant of an arbitrary quadrilateral in the plane. In particular we
show that the Hardy constant is the same as that of a certain infinite
sectorial region which has been studied by E.B. Davies.

19
The categories of this paper are: eess
25
The categories of this paper are: patt-sol
18
The categories of this paper are: econ
0
The categories of this paper are: hep-ph
26
The categories of this paper are: bayes-an
16
The categories of this paper are: stat
28
The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph
22
The categories of this paper are: chao-dyn
30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
8
The categories of this paper are: hep-ex
12
The categories of this paper are: nucl-th
36
The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat
29
The categories of this paper are: funct-an