Quick search Find article
Quick search
Find article

Unique continuation on a line for harmonic functions

Jin Cheng-+,++ and Masahiro Yamamoto-+

Show affiliations


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.


PACS

02.30.Jr Partial differential equations

02.60.Lj Ordinary and partial differential equations; boundary value problems

MSC

65Nxx Partial differential equations, boundary value problems

35J05 Laplace equation, reduced wave equation (Helmholtz), Poisson equation (See also 31Axx, 31Bxx)

Subjects

Mathematical physics

Computational physics

Dates

Issue 4 (August 1998)

Received 17 February 1998



  1. Unique continuation on a line for harmonic functions

    Jin Cheng and Masahiro Yamamoto 1998 Inverse Problems 14 869

  2. Cosmological magnetic fields

    Kerstin E Kunze 2009 J. Phys.: Conf. Ser. 189 012022

  3. Directed growth of diameter-tunable nanowires

    Birol Ozturk et al 2007 Nanotechnology 18 365302

  4. Resonances in dissociative recombination: Trends and patterns

    A E Orel et al 2009 J. Phys.: Conf. Ser. 192 012006

  5. The velocity hodograph for an arbitrary Keplerian motion

    Eugene I Butikov 2000 Eur. J. Phys. 21 297

  6. Computer-enhanced stereoscopic vision in a head-mounted operating binocular

    Wolfgang Birkfellner et al 2003 Phys. Med. Biol. 48 N49

  7. Preparation and characterization of luminescent CdS nanoparticles immobilized on poly(St-co-GMA-IDA) polymer microspheres

    Yuan-Chih Chu et al 2005 Nanotechnology 16 376

  8. Polaron effective masses with extended coherent states

    Chen Qinghu et al 1996 J. Phys.: Condens. Matter 8 3391

  9. Two-dimensional deconvolution technique to recover the original magnetic field from the flux measured by SQUID planar gradiometers

    E Andrade Lima et al 2002 Supercond. Sci. Technol. 15 1259

  10. A thin film coating for phosphor thermography

    R M Ranson et al 1998 Meas. Sci. Technol. 9 1947

Users also read

What's this?
This innovative new feature generates a list of articles 'also read' by other users based on them reading the original article. Article abstracts citations and references are all considered and weighted accordingly. We hope that this will help you find relevant papers for your research.

  1. Stability for an inverse boundary problem of determining a part of a boundary

View by subject




Export








Please login to access our web services, or create an account if you don't yet have one.

You must have cookies enabled in your web browser to be able to login.

Username
Password

Forgotten your password? Get a new one here.