Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the existence of smooth solutions for fully nonlinear elliptic
  equations with measurable "coefficients" without convexity assumptions   We show that for any uniformly elliptic fully nonlinear second-order equation
with bounded measurable "coefficients" and bounded "free" term one can find an
approximating equation which has a unique continuous and having the second
derivatives locally bounded solution in a given smooth domain with smooth
boundary data. The approximating equation is constructed in such a way that it
modifies the original one only for large values of the unknown function and its
derivatives.

8
The categories of this paper are: hep-ex
32
The categories of this paper are: atom-ph
7
The categories of this paper are: hep-th
10
The categories of this paper are: q-bio
9
The categories of this paper are: nlin
24
The categories of this paper are: dg-ga
26
The categories of this paper are: bayes-an
33
The categories of this paper are: plasm-ph
36
The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
35
The categories of this paper are: mtrl-th
19
The categories of this paper are: eess
15
The categories of this paper are: nucl-ex
20
The categories of this paper are: acc-phys
17
The categories of this paper are: q-fin
18
The categories of this paper are: econ