Carleman estimates for the Schrödinger equation and applications to an inverse problem and an observability inequality

被引：0
作者：
Ganghua Yuan
Masahiro Yamamoto
机构：
[1] Northeast Normal University,School of Mathematics and Statistics
[2] The University of Tokyo,Graduate School of Mathematical Sciences
来源：
Chinese Annals of Mathematics, Series B | 2010年 / 31卷
关键词：
Schrödinger equation; Carleman estimate; Observability inequality; Inverse problem; Unique continuation; 93B05; 35R30; 35B60;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
The authors prove Carleman estimates for the Schrödinger equation in Sobolev spaces of negative orders, and use these estimates to prove the uniqueness in the inverse problem of determining Lp-potentials. An L2-level observability inequality and unique continuation results for the Schrödinger equation are also obtained.
引用
收藏
页码：555 / 578
页数：23
相关论文
共 59 条
  • [1] Baudouin L.(2008)An inverse problem for Schrödinger equations with discontinuous main coefficient Appl. Anal. 87 1145-1165
  • [2] Mercado A.(2001)Uniqueness and stability in an inverse problem for the Schrödinger equation Inverse Problems 18 1537-1554
  • [3] Baudouin L.(2004)Global logarithmic stability in inverse hyperbolic problem by arbitrary boundary observation Inverse Problems 20 1033-1052
  • [4] Puel J. P.(2006)Logarithmic stability in determination of a coefficient in an acoustic equation by arbitrary boundary observation J. Math. Pures Appl. 85 193-224
  • [5] Bellassoued M.(1981)Global uniqueness of a class of multidimensional inverse problems Soviet Math. Dokl. 24 244-247
  • [6] Bellassoued M.(2003)Lipschitz stability in the lateral Cauchy problem for elasticity system J. Math. Kyoto Univ. 43 475-501
  • [7] Yamamoto M.(2006)Stabilization and control for the nonlinear Schrödinger equation on a compact surface Math. Z. 254 729-749
  • [8] Bukhgeim A. L.(2002)On Carleman estimates for hyperbolic equations Asymptotic Analysis 32 185-220
  • [9] Klibanov M. V.(2003)An inverse problem for the dynamical Lamé system with two sets of boundary data Comm. Pure Appl. Math. 56 1366-1382
  • [10] Cheng J.(1998)Lipschitz stability in inverse parabolic problems by the Carleman estimate Inverse Problems 14 1229-1245
123456