Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Regularity of the free boundary for the two-phase Bernoulli problem   We prove a regularity theorem for the free boundary of minimizers of the
two-phase Bernoulli problem, completing the analysis started by Alt, Caffarelli
and Friedman in the 80s. As a consequence, we also show regularity of
minimizers of the multiphase spectral optimization problem for the principal
eigenvalue of the Dirichlet Laplacian.

23
The categories of this paper are: solv-int
35
The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph
18
The categories of this paper are: econ
17
The categories of this paper are: q-fin
1
The categories of this paper are: cs
33
The categories of this paper are: plasm-ph
37
The categories of this paper are: supr-con
22
The categories of this paper are: chao-dyn
28
The categories of this paper are: alg-geom
36
The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
7
The categories of this paper are: hep-th