UNIQUE CONTINUATION ON A LINE FOR HARMONIC-FUNCTIONS

Authors
CHENG J YAMAMOTO M
Citation
J. Cheng et M. Yamamoto, UNIQUE CONTINUATION ON A LINE FOR HARMONIC-FUNCTIONS, Inverse problems, 14(4), 1998, pp. 869-882
Citations number
28
Categorie Soggetti
Mathematics,"Physycs, Mathematical","Physycs, Mathematical",Mathematics
Journal title
Inverse problems → ACNP
ISSN journal
02665611
Volume
14
Issue
4
Year of publication
1998
Pages
869 - 882
Database
ISI
SICI code
0266-5611(1998)14:4<869:UCOALF>2.0.ZU;2-D
Abstract
In this paper, we discuss local unique continuation for a harmonic fun ction on lines. By using complex extension, we prove a conditional sta bility estimation for a harmonic function on a line. Our unique contin uation is an intermediate property between the classical unique contin uation for a harmonic function and the analytic continuation for a hol omorphic function. As an application, we show conditional stability up to the boundary ill a Cauchy problem of the Laplace equation.