Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Boundary-Value Problems for the Squared Laplace Operator   The squared Laplace operator acting on symmetric rank-two tensor fields is
studied on a (flat) Riemannian manifold with smooth boundary. Symmetry of this
fourth-order elliptic operator is obtained provided that such tensor fields and
their first (or second) normal derivatives are set to zero at the boundary.
Strong ellipticity of the resulting boundary-value problems is also proved.
Mixed boundary conditions are eventually studied which involve complementary
projectors and tangential differential operators. In such a case, strong
ellipticity is guaranteed if a pair of matrices are non-degenerate. These
results find application to the analysis of quantum field theories on manifolds
with boundary.

13
The categories of this paper are: quant-ph
6
The categories of this paper are: astro-ph
18
The categories of this paper are: econ
28
The categories of this paper are: alg-geom
30
The categories of this paper are: q-alg
2
The categories of this paper are: math
23
The categories of this paper are: solv-int
20
The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio
8
The categories of this paper are: hep-ex
14
The categories of this paper are: math-ph
36
The categories of this paper are: cmp-lg
16
The categories of this paper are: stat
15
The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin