TY - JOUR
T1 - Quantitative uniqueness in the Lamé system
T2 - A step closer to optimal coefficient regularity
AU - Kuan, Rulin
AU - Lin, Ching Lung
AU - Wang, Jenn Nan
N1 - Publisher Copyright:
© 2024 Elsevier Inc.
PY - 2024/8/5
Y1 - 2024/8/5
N2 - We derive the doubling inequality and the optimal three-ball inequality for the Lamé system in the plane. The main contribution of this work is to derive these quantitative uniqueness estimates when the Lamé coefficients (μ,λ)∈W2,s(Ω)×L∞(Ω) for any fixed s>1. Consequently, we establish the strong unique continuation property (SUCP) for the Lamé system in the plane when λ is essentially bounded and μ belongs to a suitable subset of C0,γ∩W1,p with γ=2(s−1)/s and p=2s/(2−s) (note γ→0, p→2 as s→1). This result improves the early work [3] where s>4/3.
AB - We derive the doubling inequality and the optimal three-ball inequality for the Lamé system in the plane. The main contribution of this work is to derive these quantitative uniqueness estimates when the Lamé coefficients (μ,λ)∈W2,s(Ω)×L∞(Ω) for any fixed s>1. Consequently, we establish the strong unique continuation property (SUCP) for the Lamé system in the plane when λ is essentially bounded and μ belongs to a suitable subset of C0,γ∩W1,p with γ=2(s−1)/s and p=2s/(2−s) (note γ→0, p→2 as s→1). This result improves the early work [3] where s>4/3.
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U2 - 10.1016/j.jde.2024.03.027
DO - 10.1016/j.jde.2024.03.027
M3 - Article
AN - SCOPUS:85189804943
SN - 0022-0396
VL - 399
SP - 181
EP - 202
JO - Journal of Differential Equations
JF - Journal of Differential Equations
ER -