Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Tangential contact of free boundaries and the fixed boundary for
  variational solutions to a free transmission Problem   In this article we study functionals of the following type $$ \int_{\Omega}
\Big ( \langle A(x,u)\nabla u, \nabla u\rangle + \Lambda (x,u) \Big )\,dx $$
here $A(x,u)= A_+(x)\chi_{\{u>0\}}+A_-(x) \chi _{\{u\leq 0\}}$ for some
elliptic and bounded matrices $A_{\pm}$ with H\"older continuous entries and
$\Lambda(x,u) = \lambda_+(x) \chi_{\{u>0\}} + \lambda_-(x) \chi_{\{u\le 0\}}$.
We prove that the free boundaries of minimizers of the above functional touches
the fixed boundary $\partial \Omega$ in a tangential fashion, provide the graph
of boundary data touches its zeros smoothly. This assumption is reflected in
the \eqref{DPT} condition.

12
The categories of this paper are: nucl-th
37
The categories of this paper are: supr-con
34
The categories of this paper are: chem-ph
4
The categories of this paper are: cond-mat
27
The categories of this paper are: comp-gas
23
The categories of this paper are: solv-int
31
The categories of this paper are: ao-sci
5
The categories of this paper are: gr-qc
36
The categories of this paper are: cmp-lg
7
The categories of this paper are: hep-th
24
The categories of this paper are: dg-ga
1
The categories of this paper are: cs
28
The categories of this paper are: alg-geom
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
32
The categories of this paper are: atom-ph