Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Improved quantitative unique continuation for complex-valued drift
  equations in the plane   In this article, we investigate the quantitative unique continuation
properties of complex-valued solutions to drift equations in the plane. We
consider equations of the form $\Delta u + W \cdot \nabla u = 0$ in
$\mathbb{R}^2$, where $W = W_1 + i W_2$ with each $W_j$ real-valued. Under the
assumptions that $W_j \in L^{q_j}$ for some $q_1 \in [2, \infty]$, $q_2 \in (2,
\infty]$, and $W_2$ exhibits rapid decay at infinity, we prove new global
unique continuation estimates. This improvement is accomplished by reducing our
equations to vector-valued Beltrami systems. Our results rely on a novel order
of vanishing estimate combined with a finite iteration scheme.

12
The categories of this paper are: nucl-th
4
The categories of this paper are: cond-mat
19
The categories of this paper are: eess
3
The categories of this paper are: physics
30
The categories of this paper are: q-alg
18
The categories of this paper are: econ
24
The categories of this paper are: dg-ga
17
The categories of this paper are: q-fin
14
The categories of this paper are: math-ph
35
The categories of this paper are: mtrl-th
15
The categories of this paper are: nucl-ex
33
The categories of this paper are: plasm-ph
26
The categories of this paper are: bayes-an
6
The categories of this paper are: astro-ph
11
The categories of this paper are: hep-lat
5
The categories of this paper are: gr-qc