Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Comparison principles for viscosity solutions of elliptic branches of
  fully nonlinear equations independent of the gradient   The validity of the comparison principle in variable coefficient fully
nonlinear gradient free potential theory is examined and then used to prove the
comparison principle for fully nonlinear partial differential equations which
determine a suitable potential theory. The approach combines the notions of
proper elliptic branches inspired by Krylov (Trans. Amer. Math. Soc. 1995) with
the monotonicity-duality method initiated by Harvey and Lawson (Comm. Pure
Appl. Math. 2009). In the variable coefficient nonlinear potential theory, a
special role is played by the Hausdorff continuity of the proper elliptic map
$\Theta$ which defines the potential theory. In the applications to nonlinear
equations defined by an operator $F$, structural conditions on $F$ will be
determined for which there is a correspondence principle between
$\Theta$-subharmonics/superharmonics and admissible viscosity sub and
supersolutions of the nonlinear equation and for which comparison for the
equation follows from the associated compatible potential theory. General
results and explicit models of interest from differential geometry will be
examined.

6
The categories of this paper are: astro-ph
21
The categories of this paper are: adap-org
27
The categories of this paper are: comp-gas
17
The categories of this paper are: q-fin
25
The categories of this paper are: patt-sol
20
The categories of this paper are: acc-phys
22
The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
13
The categories of this paper are: quant-ph
0
The categories of this paper are: hep-ph
10
The categories of this paper are: q-bio
5
The categories of this paper are: gr-qc
8
The categories of this paper are: hep-ex
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The categories of this paper are: hep-th
34
The categories of this paper are: chem-ph
26
The categories of this paper are: bayes-an