Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Characterization of minimizable Lagrangian action functionals and a dual
  Mather theorem   We show that a necessary and sufficient condition for a smooth function on
the tangent bundle of a manifold to be a Lagrangian density whose action can be
minimized is, roughly speaking, that it be the sum of a constant, a nonnegative
function vanishing on the support of the minimizers, and an exact form.
  We show that this exact form corresponds to the differential of a Lipschitz
function on the manifold that is differentiable on the projection of the
support of the minimizers, and its derivative there is Lipschitz. This function
generalizes the notion of subsolution of the Hamilton-Jacobi equation that
appears in weak KAM theory, and the Lipschitzity result allows for the recovery
of Mather's celebrated 1991 result as a special case. We also show that our
result is sharp with several examples.
  Finally, we apply the same type of reasoning to an example of a finite
horizon Legendre problem in optimal control, and together with the Lipschitzity
result we obtain the Hamilton-Jacobi-Bellman equation and the Maximum
Principle.
  This version contains errata correcting an issue in the published version.

34
The categories of this paper are: chem-ph
6
The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc
21
The categories of this paper are: adap-org
16
The categories of this paper are: stat
37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin
12
The categories of this paper are: nucl-th
23
The categories of this paper are: solv-int
11
The categories of this paper are: hep-lat
30
The categories of this paper are: q-alg
14
The categories of this paper are: math-ph
3
The categories of this paper are: physics
26
The categories of this paper are: bayes-an
10
The categories of this paper are: q-bio
0
The categories of this paper are: hep-ph