|Title:||Liouville-type theorem for the lamÉ system with singular coefficients||Authors:||Lin, Ching Lung
|Issue Date:||1-Jan-2019||Journal Volume:||147||Journal Issue:||6||Source:||Proceedings of the American Mathematical Society||Abstract:||
©2019 Amerian Mathematial Soiety. In this paper, we study a Liouville-type theorem for the Lamé system with rough coefficients in the plane. Let u be a real-valued two-vector in R2 satisfying ∇u ∈ Lp (R2) for some p > 2 and the equation divμ ∇u + (∇u)T + ∇(λ div u) = 0 in R2. When ‖∇μ‖L2 (R2) is not large, we show that u ≡ constant in R2. As by-products, we prove the weaK unique continuation property and the uniqueness of the Cauchy problem for the Lamé system with small ‖μ‖W 1,2.
|Appears in Collections:||應用數學科學研究所|
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.