Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the set of points of smoothness for the value function for affine
  optimal control problems   We study the regularity properties of the value function associated with an
affine optimal control problem with quadratic cost plus a potential, for a
fixed final time and initial point. Without assuming any condition on singular
minimizers, we prove that the value function is continuous on an open and dense
subset of the interior of the attainable set. As a byproduct we obtain that it
is actually smooth on a possibly smaller set, still open and dense.

15
The categories of this paper are: nucl-ex
4
The categories of this paper are: cond-mat
19
The categories of this paper are: eess
9
The categories of this paper are: nlin
3
The categories of this paper are: physics
5
The categories of this paper are: gr-qc
6
The categories of this paper are: astro-ph
22
The categories of this paper are: chao-dyn
27
The categories of this paper are: comp-gas
30
The categories of this paper are: q-alg
23
The categories of this paper are: solv-int
24
The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
35
The categories of this paper are: mtrl-th
17
The categories of this paper are: q-fin
14
The categories of this paper are: math-ph