具有临界奇异势的波动方程的可观测性
Observability for wave equations with critically singular potentials
- Indian Institute of Science（印度科学学院）
- Queen Mary University of London（伦敦大学玛丽女王学院）
机构由 AI 辅助整理，请以论文原文为准。
中文总结 AI 辅助
本文针对带有临界奇异势的波动方程，结合全局Carleman估计，在满足凸性条件的有界区域上证明了适用于所有维度的边界可观测性估计。
中文摘要 AI 辅助
本文中，我们证明了在有界区域Ω⊆ℝⁿ上，带有临界奇异势（其发散为到∂Ω的逆平方距离）的波动方程的边界可观测性估计。该结果适用于所有维度，关键几何假设是Ω的凸性条件。我们结果的主要工具是全局Carleman估计，该估计被精心调整以适配势的临界奇异性质。
英文摘要
In this article, we prove boundary observability estimates for wave equations on bounded domains $Ω\subseteq \mathbb{R}^n$, with a critically singular potential that diverges as the inverse square distance to $\partial Ω$. The result is applicable in all dimensions and for wave equations with general time-dependent lower order terms. The key geometric assumption is a convexity condition on $Ω$. The main tool for our result is a global Carleman estimate that is carefully adapted to the critical singular nature of the potential.
