Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Regularity of Infinity for Elliptic Equations with Measurable
  Coefficients and Its Consequences   This paper introduces a notion of regularity (or irregularity) of the point
at infinity for the unbounded open subset of $\rr^{N}$ concerning second order
uniformly elliptic equations with bounded and measurable coefficients,
according as whether the A-harmonic measure of the point at infinity is zero
(or positive). A necessary and sufficient condition for the existence of a
unique bounded solution to the Dirichlet problem in an arbitrary open set of
$\rr^{N}, N\ge 3$ is established in terms of the Wiener test for the regularity
of the point at infinity. It coincides with the Wiener test for the regularity
of the point at infinity in the case of Laplace equation. From the topological
point of view, the Wiener test at infinity presents thinness criteria of sets
near infinity in fine topology. Precisely, the open set is a deleted
neigborhood of the point at infinity in fine topology if and only if infinity
is irregular.

22
The categories of this paper are: chao-dyn
20
The categories of this paper are: acc-phys
24
The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
14
The categories of this paper are: math-ph
17
The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat
16
The categories of this paper are: stat
18
The categories of this paper are: econ
37
The categories of this paper are: supr-con
25
The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph
33
The categories of this paper are: plasm-ph
29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
15
The categories of this paper are: nucl-ex