Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sharp norm estimates of layer potentials and operators at high frequency   In this paper, we investigate single and double layer potentials mapping
boundary data to interior functions of a domain at high frequency
$\lambda^2\to\infty$. For single layer potentials, we find that the
$L^{2}(\partial\Omega)\to{}L^{2}(\Omega)$ norms decay in $\lambda$. The rate of
decay depends on the curvature of $\partial\Omega$: The norm is
$\lambda^{-3/4}$ in general domains and $\lambda^{-5/6}$ if the boundary
$\partial\Omega$ is curved. The double layer potential, however, displays
uniform $L^{2}(\partial\Omega)\to{}L^{2}(\Omega)$ bounds independent of
curvature. By various examples, we show that all our estimates on layer
potentials are sharp.
  The appendix by Galkowski gives bounds
$L^{2}(\partial\Omega)\to{}L^{2}(\partial\Omega)$ for the single and double
layer operators at high frequency that are sharp modulo $\log \lambda$. In this
case, both the single and double layer operator bounds depend upon the
curvature of the boundary.

20
The categories of this paper are: acc-phys
27
The categories of this paper are: comp-gas
5
The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph
26
The categories of this paper are: bayes-an
21
The categories of this paper are: adap-org
15
The categories of this paper are: nucl-ex
29
The categories of this paper are: funct-an
16
The categories of this paper are: stat
23
The categories of this paper are: solv-int
13
The categories of this paper are: quant-ph
37
The categories of this paper are: supr-con
1
The categories of this paper are: cs
34
The categories of this paper are: chem-ph
24
The categories of this paper are: dg-ga
10
The categories of this paper are: q-bio