Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Pseudo-differential Operators, Transmission Problems and the Large
  Coupling Limit   In this paper we prove some new results and give new proofs of known results
related to the large coupling limit for stationary Schr\"odinger operators. The
operators we consider are of the form $-\Delta +\lambda V(x)$ where $\Delta$ is
the Laplacian, $V(x)$ is a real valued piecewise--constant potential having a
jump discontinuity across a smooth interface and $\lambda$ is the coupling
constant. Our main result is that the potential determines a non-local boundary
condition on the interface and we systematically exploit this fact to derive
various results about the large coupling problem. In particular, we obtain
estimates for convergence rates and a description of the behavior of the
spectrum of $-\Delta +\lambda V(x)$ as $\lambda\nearrow\infty$.

8
The categories of this paper are: hep-ex
15
The categories of this paper are: nucl-ex
4
The categories of this paper are: cond-mat
11
The categories of this paper are: hep-lat
6
The categories of this paper are: astro-ph
35
The categories of this paper are: mtrl-th
25
The categories of this paper are: patt-sol
33
The categories of this paper are: plasm-ph
1
The categories of this paper are: cs
9
The categories of this paper are: nlin
10
The categories of this paper are: q-bio
30
The categories of this paper are: q-alg
7
The categories of this paper are: hep-th
20
The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg
19
The categories of this paper are: eess