Analysis & PDE

  • Anal. PDE
  • Volume 9, Number 3 (2016), 515-544.

Local analytic regularity in the linearized Calderón problem

Johannes Sjöstrand and Gunther Uhlmann

Full-text: Access denied (no subscription detected)

However, an active subscription may be available with MSP at msp.org/apde.

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

We show that the linearized local Dirichlet-to-Neumann map at a real-analytic potential for measurements made at an analytic open subset of the boundary is injective.

Article information

Source
Anal. PDE, Volume 9, Number 3 (2016), 515-544.

Dates
Received: 17 December 2013
Revised: 10 August 2015
Accepted: 7 September 2015
First available in Project Euclid: 16 November 2017

Permanent link to this document
https://projecteuclid.org/euclid.apde/1510843260

Digital Object Identifier
doi:10.2140/apde.2016.9.515

Mathematical Reviews number (MathSciNet)
MR3518528

Zentralblatt MATH identifier
1342.35456

Subjects
Primary: 35R30: Inverse problems

Keywords
Calderón problem linearization partial data analytic microlocal analysis

Citation

Sjöstrand, Johannes; Uhlmann, Gunther. Local analytic regularity in the linearized Calderón problem. Anal. PDE 9 (2016), no. 3, 515--544. doi:10.2140/apde.2016.9.515. https://projecteuclid.org/euclid.apde/1510843260


Export citation

References

  • K. Astala and L. Päivärinta, “Calderón's inverse conductivity problem in the plane”, Ann. of Math. $(2)$ 163:1 (2006), 265–299.
  • A. L. Bukhgeim and G. Uhlmann, “Recovering a potential from partial Cauchy data”, Comm. Partial Differential Equations 27:3–4 (2002), 653–668.
  • D. Dos Santos Ferreira, C. E. Kenig, J. Sj östrand, and G. Uhlmann, “On the linearized local Calderón problem”, Math. Res. Lett. 16:6 (2009), 955–970.
  • B. Haberman and D. Tataru, “Uniqueness in Calderón's problem with Lipschitz conductivities”, Duke Math. J. 162:3 (2013), 497–516.
  • L. H örmander, “Fourier integral operators, I”, Acta Math. 127:1–2 (1971), 79–183. http://msp.org/idx/zbl/0212.46601Zbl 0212.46601
  • L. H örmander, An introduction to complex analysis in several variables, 3rd ed., North-Holland Mathematical Library 7, North-Holland, Amsterdam, 1990.
  • O. Y. Imanuvilov and M. Yamamoto, “Inverse boundary value problem for the Schrödinger equation in a cylindrical domain by partial boundary data”, Inverse Problems 29:4 (2013), 045002.
  • O. Y. Imanuvilov, G. Uhlmann, and M. Yamamoto, “The Calderón problem with partial data in two dimensions”, J. Amer. Math. Soc. 23:3 (2010), 655–691.
  • V. Isakov, “On uniqueness in the inverse conductivity problem with local data”, Inverse Probl. Imaging 1:1 (2007), 95–105.
  • C. Kenig and M. Salo, “The Calderón problem with partial data on manifolds and applications”, Anal. PDE 6:8 (2013), 2003–2048.
  • C. Kenig and M. Salo, “Recent progress in the Calderón problem with partial data”, pp. 193–222 in Inverse problems and applications (Irvine, CA and Hangzhou, China, 2012), edited by P. Stefanov et al., Contemp. Math. 615, Amer. Math. Soc., Providence, RI, 2014.
  • C. E. Kenig, J. Sj östrand, and G. Uhlmann, “The Calderón problem with partial data”, Ann. of Math. $(2)$ 165:2 (2007), 567–591.
  • R. Kohn and M. Vogelius, “Determining conductivity by boundary measurements”, Comm. Pure Appl. Math. 37:3 (1984), 289–298.
  • J. M. Lee and G. Uhlmann, “Determining anisotropic real-analytic conductivities by boundary measurements”, Comm. Pure Appl. Math. 42:8 (1989), 1097–1112.
  • A. I. Nachman, “Global uniqueness for a two-dimensional inverse boundary value problem”, Ann. of Math. $(2)$ 143:1 (1996), 71–96.
  • J. Sj östrand, “Singularités analytiques microlocales”, pp. 1–166 in Astérisque, Astérisque 95, Soc. Math. France, Paris, 1982.
  • J. Sj östrand, “Geometric bounds on the density of resonances for semiclassical problems”, Duke Math. J. 60:1 (1990), 1–57.
  • J. Sylvester and G. Uhlmann, “A uniqueness theorem for an inverse boundary value problem in electrical prospection”, Comm. Pure Appl. Math. 39:1 (1986), 91–112.
  • J. Sylvester and G. Uhlmann, “A global uniqueness theorem for an inverse boundary value problem”, Ann. of Math. $(2)$ 125:1 (1987), 153–169.
  • G. Uhlmann, “Electrical impedance tomography and Calderón's problem”, Inverse Problems 25:12 (2009), 123011.