 
Summary: SNSMathPreprintServerhttp://math.sns.it/papers/lastrizha03/
J. Inv. IllPosed Problems, Vol. 11, No. 3, pp. 196 (2003)
c VSP 2003
Global Uniqueness, Observability and Stabilization of Nonconserva
tive Schršodinger Equations Via Pointwise Carleman Estimates
I. LASIECKA,
R. TRIGGIANI,
and X. ZHANG
Received November 29, 2002
Abstract  We consider a general nonconservative Schršodinger equation defined on an open bounded domain in Rn
,
with C2
boundary = = 0 1, 0 1 = , subject to (Dirichlet and, as a main focus, to) Neumann boundary
conditions on the entire boundary . Here, 0 and 1 are the unobserved (or uncontrolled) and observed (or controlled)
parts of the boundary, respectively, both being relatively open in . The Schršodinger equation includes energylevel
(H1
()level) terms, which accordingly may be viewed as unbounded perturbations. The first goal of the paper is to
provide Carlemantype inequalities at the H1
level, which do not contain lowerorder terms; this is a distinguishing
feature over most of the literature. This goal is accomplished in a few steps: the paper obtains first pointwise Carleman
