Observability for Wave Equations with Critically Singular Potentials
Vaibhav Kumar Jena, Arick Shao
Abstract
In this article, we prove boundary observability estimates for wave equations on bounded domains Ω⊂eq Rn, with a critically singular potential that diverges as the inverse square distance to ∂ Ω. The result is applicable in all dimensions, and 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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