Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: H\"older estimates for the Neumann problem in a domain with holes and a
  relation formula between the Dirichlet and Neumann problems   In this paper we study the dependence of the H\"older estimates on the
geometry of a domain with holes for the Neumann problem. For this, we study the
H\"older regularity of the solutions to the Dirichlet and Neumann problems in
the disk (and in the exterior of the disk), from which we get a relation
between harmonic extensions and harmonic functions with prescribed Neumann
condition on the boundary of the disk (for both interior and exterior
problems).

32
The categories of this paper are: atom-ph
9
The categories of this paper are: nlin
3
The categories of this paper are: physics
37
The categories of this paper are: supr-con
25
The categories of this paper are: patt-sol
11
The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph
27
The categories of this paper are: comp-gas
16
The categories of this paper are: stat
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat
15
The categories of this paper are: nucl-ex
8
The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio
28
The categories of this paper are: alg-geom
29
The categories of this paper are: funct-an