Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An integration by parts formula for the bilinear form of the
  hypersingular boundary integral operator for the transient heat equation in
  three spatial dimensions   While an integration by parts formula for the bilinear form of the
hypersingular boundary integral operator for the transient heat equation in
three spatial dimensions is available in the literature, a proof of this
formula seems to be missing. Moreover, the available formula contains an
integral term including the time derivative of the fundamental solution of the
heat equation, whose interpretation is difficult at second glance. To fill
these gaps we provide a rigorous proof of a general version of the integration
by parts formula and an alternative representation of the mentioned integral
term, which is valid for a certain class of functions including the typical
tensor-product discretization spaces.

20
The categories of this paper are: acc-phys
37
The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat
23
The categories of this paper are: solv-int
10
The categories of this paper are: q-bio
24
The categories of this paper are: dg-ga
33
The categories of this paper are: plasm-ph
16
The categories of this paper are: stat
11
The categories of this paper are: hep-lat
36
The categories of this paper are: cmp-lg
34
The categories of this paper are: chem-ph
14
The categories of this paper are: math-ph
18
The categories of this paper are: econ
7
The categories of this paper are: hep-th
27
The categories of this paper are: comp-gas
22
The categories of this paper are: chao-dyn