Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Analysis of Optimal Control Problems with an $L^0$ Term in the Cost
  Functional   In this paper, we investigate optimal control problems subject to a
semilinear elliptic partial differential equations. The cost functional
contains a term that measures the size of the support of the control, which is
the so-called $L^0$-norm. We provide necessary and sufficient optimality
conditions of second-order. The sufficient second-order condition is obtained
by analyzing a partially convexified problem. Interestingly, the structure of
the problem yields second-order conditions with different bilinear forms for
the necessary and for the sufficient condition.

31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
5
The categories of this paper are: gr-qc
7
The categories of this paper are: hep-th
9
The categories of this paper are: nlin
15
The categories of this paper are: nucl-ex
14
The categories of this paper are: math-ph
34
The categories of this paper are: chem-ph
10
The categories of this paper are: q-bio
21
The categories of this paper are: adap-org
11
The categories of this paper are: hep-lat
37
The categories of this paper are: supr-con
1
The categories of this paper are: cs
20
The categories of this paper are: acc-phys
24
The categories of this paper are: dg-ga