Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An optimal design problem with non-standard growth and no concentration
  effects   We obtain an integral representation for certain functionals arising in the
context of optimal design and damage evolution problems under non-standard
growth conditions and perimeter penalisation. Under our hypotheses, the
integral representation includes a term which is absolutely continuous with
respect to the Lebesgue measure and a perimeter term, but no additional
singular term.
  We also study some dimension reduction problems providing results for the
optimal design of thin films.

13
The categories of this paper are: quant-ph
29
The categories of this paper are: funct-an
35
The categories of this paper are: mtrl-th
18
The categories of this paper are: econ
14
The categories of this paper are: math-ph
9
The categories of this paper are: nlin
19
The categories of this paper are: eess
20
The categories of this paper are: acc-phys
6
The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc
34
The categories of this paper are: chem-ph
31
The categories of this paper are: ao-sci
1
The categories of this paper are: cs
7
The categories of this paper are: hep-th
26
The categories of this paper are: bayes-an
32
The categories of this paper are: atom-ph