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Observability for wave equations with critically singular potentials
Abstract
In this article, we prove boundary observability estimates for wave equations on bounded domains Ω⊆ ℝn, with a critically singular potential that diverges as the inverse square distance to ∂ 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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BibTeX
@misc{jena2026observability,
title = {{Observability for wave equations with critically singular potentials}},
author = {Vaibhav Kumar Jena and Arick Shao},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.28132},
eprint = {2608.28132},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.28132},
}
RIS
TY - UNPB
TI - Observability for wave equations with critically singular potentials
AU - Vaibhav Kumar Jena
AU - Arick Shao
PY - 2026
DA - 2026/09/18
PB - arXiv
DO - 10.48550/arxiv.2608.28132
UR - https://arxiv.org/abs/2608.28132
AB - In this article, we prove boundary observability estimates for wave equations on bounded domains Ω⊆ ℝ^n, with a critically singular potential that diverges as the inverse square distance to ∂ 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.
ER -