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arXiv · 2608.28132

Observability for wave equations with critically singular potentials

Vaibhav Kumar Jena·Arick Shao
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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.

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Vaibhav Kumar Jena, Arick Shao. 2026-09-18. Observability for wave equations with critically singular potentials. https://arxiv.org/abs/2608.28132

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