Year: 2026
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Authors: Jena, Vaibhav Kumar, Shao, Arick
Institution: Queen Mary University of London
Subfield: Control and Systems Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7204849656
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