Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Shape optimization problems in control form   We consider a shape optimization problem written in the optimal control form:
the governing operator is the $p$-Laplacian in the Euclidean space $\R^d$, the
cost is of an integral type, and the control variable is the domain of the
state equation. Conditions that guarantee the existence of an optimal domain
will be discussed in various situations. It is proved that the optimal domains
have a finite perimeter and, under some suitable assumptions, that they are
open sets. A crucial difference is between the case $p>d$, where the existence
occurs under very mild conditions, and the case $p\le d$, where additional
assumptions have to be made on the data.

33
The categories of this paper are: plasm-ph
1
The categories of this paper are: cs
18
The categories of this paper are: econ
36
The categories of this paper are: cmp-lg
37
The categories of this paper are: supr-con
15
The categories of this paper are: nucl-ex
20
The categories of this paper are: acc-phys
26
The categories of this paper are: bayes-an
32
The categories of this paper are: atom-ph
0
The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
9
The categories of this paper are: nlin
28
The categories of this paper are: alg-geom
23
The categories of this paper are: solv-int
22
The categories of this paper are: chao-dyn