Jin Cheng and Masahiro Yamamoto 1998 Inverse Problems 14 869 doi:10.1088/0266-5611/14/4/007
Jin Cheng
,
and Masahiro Yamamoto![]()
In this paper, we discuss local unique continuation for a harmonic function on lines. By using complex extension, we prove a conditional stability estimation for a harmonic function on a line. Our unique continuation is an intermediate property between the classical unique continuation for a harmonic function and the analytic continuation for a holomorphic function. As an application, we show conditional stability up to the boundary in a Cauchy problem of the Laplace equation.
02.30.Jr Partial differential equations
02.60.Lj Ordinary and partial differential equations; boundary value problems
65Nxx Partial differential equations, boundary value problems
35J05 Laplace equation, reduced wave equation (Helmholtz), Poisson equation (See also 31Axx, 31Bxx)
Issue 4 (August 1998)
Received 17 February 1998
Jin Cheng and Masahiro Yamamoto 1998 Inverse Problems 14 869
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