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Uniform boundary observability for periodic wave equations with low frequency exponent 4/3
Abstract
We study boundary observability for Dirichlet wave equations with symmetric, periodic coefficients in bounded C2,1 domains of dimension d≥2. We establish two-sided observability estimates, uniform in the oscillation scale ε, for initial data generated by eigenfunctions with eigenvalues at most δε−4/3 with some small factor δ. The proof reduces wave observability to boundary gradient estimates for narrow spectral clusters. These estimates are obtained using a second-order expansion and a uniform commutator estimate for harmonic extension in boundary layers.
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BibTeX
@misc{huang2026uniform,
title = {{Uniform boundary observability for periodic wave equations with low frequency exponent $4/3$}},
author = {Zhonggan Huang and Jinping Zhuge},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.04661},
eprint = {2611.04661},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.04661},
}
RIS
TY - UNPB
TI - Uniform boundary observability for periodic wave equations with low frequency exponent 4/3
AU - Zhonggan Huang
AU - Jinping Zhuge
PY - 2026
DA - 2026/11/03
PB - arXiv
DO - 10.48550/arxiv.2611.04661
UR - https://arxiv.org/abs/2611.04661
AB - We study boundary observability for Dirichlet wave equations with symmetric, periodic coefficients in bounded C^2,1 domains of dimension d≥2. We establish two-sided observability estimates, uniform in the oscillation scale ε, for initial data generated by eigenfunctions with eigenvalues at most δε^−4/3 with some small factor δ. The proof reduces wave observability to boundary gradient estimates for narrow spectral clusters. These estimates are obtained using a second-order expansion and a uniform commutator estimate for harmonic extension in boundary layers.
ER -