Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lower semicontinuous envelopes in $w^{1,1}\times l^p$   It is studied the lower semicontinuity of functionals of the type
$\int_\Omega f(x,u,v, \nabla u)dx$ with respect to the $(W^{1,1}\times
L^p)$-weak \ast topology. Moreover in absence of lower semicontinuity, it is
also provided an integral representation in $W^{1,1} \times L^p$ for the lower
semicontinuous envelope.

8
The categories of this paper are: hep-ex
13
The categories of this paper are: quant-ph
32
The categories of this paper are: atom-ph
11
The categories of this paper are: hep-lat
24
The categories of this paper are: dg-ga
5
The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph
21
The categories of this paper are: adap-org
1
The categories of this paper are: cs
26
The categories of this paper are: bayes-an
31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
15
The categories of this paper are: nucl-ex
20
The categories of this paper are: acc-phys
37
The categories of this paper are: supr-con
19
The categories of this paper are: eess