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arXiv · 2611.04661

Uniform boundary observability for periodic wave equations with low frequency exponent $4/3$

Zhonggan Huang·Jinping Zhuge
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Abstract

We study boundary observability for Dirichlet wave equations with symmetric, periodic coefficients in bounded $C^{2,1}$ domains of dimension $d\ge2$. We establish two-sided observability estimates, uniform in the oscillation scale $\varepsilon$, for initial data generated by eigenfunctions with eigenvalues at most $δ\varepsilon^{-4/3}$ 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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Zhonggan Huang, Jinping Zhuge. 2026-11-03. Uniform boundary observability for periodic wave equations with low frequency exponent $4/3$. https://arxiv.org/abs/2611.04661

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