Publication Cover
Applicable Analysis
An International Journal
Volume 99, 2020 - Issue 5
88
Views
2
CrossRef citations to date
0
Altmetric
Articles

Single logarithmic conditional stability in determining unknown boundaries

, &
Pages 725-746 | Received 18 Mar 2018, Accepted 26 Jul 2018, Published online: 28 Aug 2018

References

  • Andrieux S, Abda AB, Jaoua M. Identifiabilité de frontière inaccesible par des measures de surface. C R Acad Sci Paris Sér I Math. 1993;316:429–434.
  • Aparicio ND, Pidcock MK. The boundary inverse problem for the Laplace equation in two dimensions. Inverse Probl. 1996;12:565–577. doi: 10.1088/0266-5611/12/5/003
  • Kaup PG, Santosa F, Vogelius M. Method for imaging corrosion damage in thin plates from electrostatic data. Inverse Probl. 1996;12:279–293. doi: 10.1088/0266-5611/12/3/008
  • McIver M. Characterization of surface-breaking cracks in metal sheets by using AC electric fields. Proc R Soc London A. 1989;421:179–194. doi: 10.1098/rspa.1989.0008
  • McIver M. An inverse problem in electro-magnetic crack detection. IMA J Appl Math. 1991;47:127–145. doi: 10.1093/imamat/47.2.127
  • Alessandrini G, Beretta E, Rosset E, et al. Optimal stability for inverse elliptic boundary value problems with unknown boundaries. Ann Scuola Norm Sup Pisa Cl Sci. 2000;29:755–806.
  • Alessandrini G, Morassi A. Strong unique continuation for the Lamé system of elasticity. Comm Partial Diff Eqs. 2001;26:1787–1810. doi: 10.1081/PDE-100107459
  • Beretta E, Vessella S. Stable determination of boundaries from Cauchy data. SIAMJMath Anal. 1998;30:220–232.
  • Bukhgeim AL, Cheng J, Yamamoto M. Uniqueness and stability for an inverse problem of determining parts of boundary. In: Tanaka M, Dulikravich GS, editors. Inverse problems in engineering mechanics. Amsterdam: Elsevier; 1998. p. 327–336.
  • Bukhgeim AL, Cheng J, Yamamoto M. Stability for an inverse boundary problem of determining a part of boundary. Inverse Probl. 1999;14:1021–1032. doi: 10.1088/0266-5611/15/4/312
  • Cheng J, Hon YC, Yamamoto M. Conditional stability estimation for an inverse boundary problem with non-smooth boundary in R3. Trans Am Math Soc. 2001;353:4123–4139. doi: 10.1090/S0002-9947-01-02758-1
  • Colton D, Kress R. Inverse acoustic and electromagnetic scattering theory. New York (NY): Springer; 1998.
  • Colton D, Sleeman BD. Uniqueness theorems for the inverse problem of acoustic scattering. IMA J Appl Math. 1983;31:253–259. doi: 10.1093/imamat/31.3.253
  • Stefanov P, Uhlmann G. Local uniqueness for the fixed energy fixed angle inverse problem in obstacle scattering. Proc Amer Math Soc. 2004;132:1351–1354. doi: 10.1090/S0002-9939-03-07363-5
  • Isakov V. New stability results for soft obstacles in inverse scattering. Inverse Probl. 1993;9:535–543. doi: 10.1088/0266-5611/9/5/003
  • Sincich E, Sini M. Local stability for soft obstacles by a single measurement. Inverse Probl Imaging. 2008;2:301–315. doi: 10.3934/ipi.2008.2.301
  • Gintides D. Local uniqueness for the inverse scattering problem in acoustics via the Faber-Krahn inequality. Inverse Probl. 2005;21:1195–1205. doi: 10.1088/0266-5611/21/4/001
  • Hu G, Yamamoto M. Hölder stability estimate of the Robin coefficient in corrosion detection problems with a single boundary measurement. Inverse Probl. 2015;31:115009. doi: 10.1088/0266-5611/31/11/115009
  • Gilbarg D, Trudinger N. Elliptic partial differential equations of second order. Heidelberg: Springer-Verlag; 1977.
  • Sincich E. Stable determination of the surface impedance of an obstacle by far field measurements. SIAM J Math Anal. 2006;38:434–451. doi: 10.1137/050631513
  • Hörmander L. Linear partial differential operators. New York: Springer-Verlag; 1963.
  • Isakov V. Inverse source problems. Rhode Island: Providence; 1990.
  • Isakov V. Inverse problems for partial differential equations. New York (NY): Springer; 2006.
  • Imanuvilov OYu., Yamamoto M. Lipschitz stability in inverse parabolic problems by the Carleman estimate. Inverse Probl. 1998;14:1229–1245. doi: 10.1088/0266-5611/14/5/009
  • Imanuvilov OY. Controllability of parabolic equations. Sbornik Math. 1995;186:879–900. doi: 10.1070/SM1995v186n06ABEH000047
  • Bellassoued M, Yamamoto M. Logarithmic stability in determination of a coefficient in an acoustic equation by arbitrary boundary observation. J Math Pures Appl. 2006;85:193–224. doi: 10.1016/j.matpur.2005.02.004
  • Komornik V. Exact controllability and stabilization: the multiplier method. Chichester: Wiley; 1994.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.