Observability for Wave Equations with Critically Singular Potentials

Vaibhav Kumar Jena; Arick Shao

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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 $\Omega \subseteq \mathbb{R}^n$, with a critically singular potential that diverges as the inverse square distance to $\partial \Omega$. The result is applicable in all dimensions, and the key geometric assumption is a convexity condition on $\Omega$. 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. 2026-08-28. Observability for Wave Equations with Critically Singular Potentials. https://arxiv.org/abs/2608.28132

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