Quantitative uniqueness in the Lamé system: A step closer to optimal coefficient regularity

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.