Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The simultaneous asymmetric perturbation method for overdetermined free
  boundary problems   In this paper, we introduce a new method for applying the implicit function
theorem to find nontrivial solutions to overdetermined problems with a fixed
boundary (given) and a free boundary (to be determined). The novelty of this
method lies in the kind of perturbations considered. Indeed, we work with
perturbations that exhibit different levels of regularity on each boundary.
This allows us to construct solutions that would have been out of reach
otherwise. Another benefit of this method lies in the improvement of the
regularity gap between the free boundary and the given one. Finally, some
geometric properties of the solutions, such as symmetry and convexity, are also
discussed.

27
The categories of this paper are: comp-gas
14
The categories of this paper are: math-ph
5
The categories of this paper are: gr-qc
16
The categories of this paper are: stat
24
The categories of this paper are: dg-ga
33
The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
34
The categories of this paper are: chem-ph
1
The categories of this paper are: cs
28
The categories of this paper are: alg-geom
6
The categories of this paper are: astro-ph
12
The categories of this paper are: nucl-th
13
The categories of this paper are: quant-ph
29
The categories of this paper are: funct-an
32
The categories of this paper are: atom-ph
3
The categories of this paper are: physics