Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Existence and regularity results for the penalized thin obstacle problem
  with variable coefficients   In this paper we give a comprehensive treatment of a two-penalty boundary
obstacle problem for a divergence form elliptic operator, motivated by
applications to fluid dynamics and thermics. Specifically, we prove existence,
uniqueness and optimal regularity of solutions, and establish structural
properties of the free boundary. The proofs are based on tailor-made
monotonicity formulas of Almgren, Weiss, and Monneau-type, combined with the
classical theory of oblique derivative problems.

12
The categories of this paper are: nucl-th
9
The categories of this paper are: nlin
15
The categories of this paper are: nucl-ex
22
The categories of this paper are: chao-dyn
30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas
6
The categories of this paper are: astro-ph
0
The categories of this paper are: hep-ph
16
The categories of this paper are: stat
32
The categories of this paper are: atom-ph
10
The categories of this paper are: q-bio
24
The categories of this paper are: dg-ga
18
The categories of this paper are: econ
11
The categories of this paper are: hep-lat
5
The categories of this paper are: gr-qc
19
The categories of this paper are: eess