Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Analysis of blow-ups for the double obstacle problem in dimension two   In this article we study a normalised double obstacle problem with polynomial
obstacles $ p^1\leq p^2$ under the assumption that $ p^1(x)=p^2(x)$ iff $ x=0$.
In dimension two we give a complete characterisation of blow-up solutions
depending on the coefficients of the polynomials $p^1, p^2$. In particular, we
see that there exists a new type of blow-ups, that we call double-cone
solutions since the coincidence sets $\{u=p^1\}$ and $\{u=p^2\}$ are cones with
a common vertex. We prove the uniqueness of blow-up limits, and analyse the
regularity of the free boundary in dimension two. In particular we show that if
the solution to the double obstacle problem has a double-cone blow-up limit at
the origin, then locally the free boundary consists of four
$C^{1,\gamma}$-curves, meeting at the origin. In the end we give an example of
a three-dimensional double-cone solution.

37
The categories of this paper are: supr-con
18
The categories of this paper are: econ
3
The categories of this paper are: physics
4
The categories of this paper are: cond-mat
5
The categories of this paper are: gr-qc
27
The categories of this paper are: comp-gas
34
The categories of this paper are: chem-ph
6
The categories of this paper are: astro-ph
0
The categories of this paper are: hep-ph
11
The categories of this paper are: hep-lat
28
The categories of this paper are: alg-geom
21
The categories of this paper are: adap-org
16
The categories of this paper are: stat
33
The categories of this paper are: plasm-ph
1
The categories of this paper are: cs
23
The categories of this paper are: solv-int