Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An optimization problem in thermal insulation with Robin boundary
  conditions   We study thermal insulating of a bounded body $\Omega\subset \mathbb{R}^n$.
Under a prescribed heat source $f\geq 0$, we consider a model of heat transfer
between $\Omega$ and the environment determined by convection; this
corresponds, before insulation, to Robin boundary conditions. The body is then
surrounded by a layer of insulating material of thickness of size
$\varepsilon>0$, and whose conductivity is also proportional to $\varepsilon$.
This corresponds to the case of a small amount of insulating material, with
excellent insulating properties. We then compute the $\Gamma$-limit of the
energy functional $F_\varepsilon$ and prove that this is a functional $F$ whose
minimizers still satisfy an elliptic PDEs system with a non uniform Robin
boundary condition depending on the distribution of insulating layer around
$\Omega$. In a second step we study the maximization of heat content (which
measures the goodness of the insulation) among all the possible distributions
of insulating material with fixed mass, and prove an optimal upper bound in
terms of geometric properties. Eventually we prove a conjecture which states
that the ball surrounded by a uniform distribution of insulating material
maximizes the heat content.

27
The categories of this paper are: comp-gas
32
The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
11
The categories of this paper are: hep-lat
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The categories of this paper are: chao-dyn
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The categories of this paper are: alg-geom
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The categories of this paper are: bayes-an
5
The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: acc-phys
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The categories of this paper are: q-bio
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The categories of this paper are: plasm-ph
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The categories of this paper are: math-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: cmp-lg