Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Asymptotic Expansion for Harmonic Functions in the Half-Space with a
  Pressurized Cavity   In this paper, we address a simplified version of a problem arising from
volcanology. Specifically, as reduced form of the boundary value problem for
the Lam\'e system, we consider a Neumann problem for harmonic functions in the
half-space with a cavity $C$. Zero normal derivative is assumed at the boundary
of the half-space; differently, at $\partial C$, the normal derivative of the
function is required to be given by an external datum $g$, corresponding to a
pressure term exerted on the medium at $\partial C$. Under the assumption that
the (pressurized) cavity is small with respect to the distance from the
boundary of the half-space, we establish an asymptotic formula for the solution
of the problem. Main ingredients are integral equation formulations of the
harmonic solution of the Neumann problem and a spectral analysis of the
integral operators involved in the problem. In the special case of a datum $g$
which describes a constant pressure at $\partial C$, we recover a simplified
representation based on a polarization tensor.

37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin
28
The categories of this paper are: alg-geom
3
The categories of this paper are: physics
22
The categories of this paper are: chao-dyn
8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
10
The categories of this paper are: q-bio
15
The categories of this paper are: nucl-ex
27
The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph
12
The categories of this paper are: nucl-th
33
The categories of this paper are: plasm-ph
11
The categories of this paper are: hep-lat
25
The categories of this paper are: patt-sol
32
The categories of this paper are: atom-ph