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SNSMathPreprintServer-http://math.sns.it/papers/lastrizha03/ J. Inv. Ill-Posed Problems, Vol. 11, No. 3, pp. 196 (2003)

Summary: SNSMathPreprintServer-http://math.sns.it/papers/lastrizha03/
J. Inv. Ill-Posed 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
and X. ZHANG
Received November 29, 2002
Abstract -- We consider a general non-conservative 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 energy-level
()-level) terms, which accordingly may be viewed as unbounded perturbations. The first goal of the paper is to
provide Carleman-type inequalities at the H1
-level, which do not contain lower-order 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


Source: Abbondandolo, Alberto - Scuola Normale Superiore of Pisa


Collections: Mathematics