论文标题
改进了平面中复杂值漂移方程的定量独特延续
Improved quantitative unique continuation for complex-valued drift equations in the plane
论文作者
论文摘要
在本文中，我们研究了复杂值解决方案在平面中漂移方程的定量独特延续性。我们考虑了$ \ \ nabla u = 0 $ in $ \ mathbb {r}^2 $，其中$ w = w_1 + i w_2 $，每个$ w_j $ real-valueD的等式的方程式。假设在l^{q_j} $中，对于某些$ q_1 \ in [2，\ infty] $，\ infty] $，$ q_2 \ in（2，\ infty] $和$ w_2 $在无限属处表现出快速衰减的快速衰减。消失的估计与有限迭代方案相结合。
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 $Δu + W \cdot \nabla u = 0$ 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.
