Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Lipschitz stable reconstruction formula for the inverse problem for
  the wave equation   We consider the problem to reconstruct a wave speed $c \in C^\infty(M)$ in a
domain $M \subset \R^n$ from acoustic boundary measurements modelled by the
hyperbolic Dirichlet-to-Neumann map $\Lambda$. We introduce a reconstruction
formula for $c$ that is based on the Boundary Control method and incorporates
features also from the complex geometric optics solutions approach. Moreover,
we show that the reconstruction formula is locally Lipschitz stable for a low
frequency component of $c^{-2}$ under the assumption that the Riemannian
manifold $(M, c^{-2} dx^2)$ has a strictly convex function with no critical
points. That is, we show that for all bounded $C^2$ neighborhoods $U$ of $c$,
there is a $C^1$ neighborhood $V$ of $c$ and constants $C, R > 0$ such that
|\F\ll(\tilde c^{-2} - c^{-2}\rr)(\xi)| \le C e^{2R |\xi|} \norm{\tilde \Lambda
- \Lambda}_*, \quad \xi \in \R^n, for all $\tilde c \in U \cap V$, where
$\tilde \Lambda$ is the Dirichlet-to-Neumann map corresponding to the wave
speed $\tilde c$ and $\norm{\cdot}_*$ is a norm capturing certain regularity
properties of the Dirichlet-to-Neumann maps.

4
The categories of this paper are: cond-mat
13
The categories of this paper are: quant-ph
3
The categories of this paper are: physics
0
The categories of this paper are: hep-ph
34
The categories of this paper are: chem-ph
22
The categories of this paper are: chao-dyn
27
The categories of this paper are: comp-gas
25
The categories of this paper are: patt-sol
24
The categories of this paper are: dg-ga
19
The categories of this paper are: eess
28
The categories of this paper are: alg-geom
9
The categories of this paper are: nlin
31
The categories of this paper are: ao-sci
18
The categories of this paper are: econ
21
The categories of this paper are: adap-org
10
The categories of this paper are: q-bio