Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stationary states to a free boundary transmission problem for an
  electrostatically actuated plate   A two-dimensional free boundary transmission problem arising in the modeling
of an electrostatically actuated plate is considered and a representation
formula for the derivative of the associated electrostatic energy with respect
to the deflection of the plate is derived. The latter paves the way for the
construction of energy minimizers and also provides the Euler-Lagrange equation
satisfied by these minimizers. A by-product is the monotonicity of the
electrostatic energy with respect to the deflection.

9
The categories of this paper are: nlin
36
The categories of this paper are: cmp-lg
17
The categories of this paper are: q-fin
3
The categories of this paper are: physics
10
The categories of this paper are: q-bio
0
The categories of this paper are: hep-ph
15
The categories of this paper are: nucl-ex
29
The categories of this paper are: funct-an
33
The categories of this paper are: plasm-ph
34
The categories of this paper are: chem-ph
11
The categories of this paper are: hep-lat
21
The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat
12
The categories of this paper are: nucl-th
23
The categories of this paper are: solv-int
7
The categories of this paper are: hep-th