Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spectral asymptotics for nonsmooth singular Green operators   Singular Green operators G appear typically as boundary correction terms in
resolvents for elliptic boundary value problems on a domain \Omega \subset R^n,
and more generally they appear in the calculus of pseudodifferential boundary
problems. In particular, the boundary term in a Krein resolvent formula is a
singular Green operator. It is well-known in smooth cases that when G is of
negative order -t on a bounded domain, its eigenvalues or s-numbers have the
behavior (*) s_j(G) \sim c j^{-t/(n-1)} for j\to \infty, governed by the
boundary dimension n-1. In some nonsmooth cases, upper estimates (**) s_j(G)
\le Cj^{-t/(n-1)} are known.
  We show that (*) holds when G is a general selfadjoint nonnegative singular
Green operator with symbol merely H\"older continuous in x. We also show (*)
with t=2 for the boundary term in the Krein resolvent formula comparing the
Dirichlet and a Neumann-type problem for a strongly elliptic second-order
differential operator (not necessarily selfadjoint) with coefficients in
W^1_p(\Omega) for some p>n.

14
The categories of this paper are: math-ph
34
The categories of this paper are: chem-ph
25
The categories of this paper are: patt-sol
8
The categories of this paper are: hep-ex
29
The categories of this paper are: funct-an
5
The categories of this paper are: gr-qc
11
The categories of this paper are: hep-lat
36
The categories of this paper are: cmp-lg
17
The categories of this paper are: q-fin
0
The categories of this paper are: hep-ph
3
The categories of this paper are: physics
37
The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom
19
The categories of this paper are: eess
12
The categories of this paper are: nucl-th
1
The categories of this paper are: cs