Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Monotonicity-based inversion of the fractional Schr\"odinger equation
  II. General potentials and stability   In this work, we use monotonicity-based methods for the fractional
Schr\"odinger equation with general potentials $q\in L^\infty(\Omega)$ in a
Lipschitz bounded open set $\Omega\subset \mathbb R^n$ in any dimension $n\in
\mathbb N$. We demonstrate that if-and-only-if monotonicity relations between
potentials and the Dirichlet-to-Neumann map hold up to a finite dimensional
subspace. Based on these if-and-only-if monotonicity relations, we derive a
constructive global uniqueness results for the fractional Calder\'on problem
and its linearized version. We also derive a reconstruction method for unknown
obstacles in a given domain that only requires the background solution of the
fractional Schr\"odinger equation, and we prove uniqueness and Lipschitz
stability from finitely many measurements for potentials lying in an a-priori
known bounded set in a finite dimensional subset of $L^\infty(\Omega)$.

21
The categories of this paper are: adap-org
26
The categories of this paper are: bayes-an
15
The categories of this paper are: nucl-ex
10
The categories of this paper are: q-bio
24
The categories of this paper are: dg-ga
13
The categories of this paper are: quant-ph
17
The categories of this paper are: q-fin
16
The categories of this paper are: stat
7
The categories of this paper are: hep-th
1
The categories of this paper are: cs
23
The categories of this paper are: solv-int
19
The categories of this paper are: eess
30
The categories of this paper are: q-alg
20
The categories of this paper are: acc-phys
6
The categories of this paper are: astro-ph
3
The categories of this paper are: physics