Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Poinca\'e type inequalities for vector functions with zero mean normal
  traces on the boundary and applications to interpolation methods   In the paper, we consider inequalities of the Poincar\'e--Steklov type for
subspaces of $H^1$-functions defined in a bounded domain $\Omega\in \Rd$ with
Lipschitz boundary $\partial\Omega$. For scalar valued functions, the subspaces
are defined by zero mean condition on $\partial\Omega$ or on a part of
$\partial\Omega$ having positive $d-1$ measure. For vector valued functions,
zero mean conditions are imposed on components (e.g., normal components) of the
function on certain $d-1$ dimensional manifolds (e.g., on plane or curvilinear
faces of $\partial\Omega$).
  We find explicit and simply computable bounds of the respective constants for
domains typically used in finite element methods (triangles, quadrilaterals,
tetrahedrons, prisms, pyramids, and domains composed of them). The second part
of the paper discusses applications of the estimates to interpolation of scalar
and vector valued functions. %383838

22
The categories of this paper are: chao-dyn
23
The categories of this paper are: solv-int
13
The categories of this paper are: quant-ph
7
The categories of this paper are: hep-th
18
The categories of this paper are: econ
20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph
14
The categories of this paper are: math-ph
11
The categories of this paper are: hep-lat
12
The categories of this paper are: nucl-th
10
The categories of this paper are: q-bio
1
The categories of this paper are: cs
34
The categories of this paper are: chem-ph
30
The categories of this paper are: q-alg
37
The categories of this paper are: supr-con
31
The categories of this paper are: ao-sci