Publication Cover
Applicable Analysis
An International Journal
Volume 95, 2016 - Issue 11
166
Views
8
CrossRef citations to date
0
Altmetric
Articles

Determination of lower order perturbations of the polyharmonic operator from partial boundary data

&
Pages 2444-2463 | Received 05 May 2015, Accepted 07 Sep 2015, Published online: 06 Oct 2015

References

  • Grubb G. Distributions and operators. Vol. 252, Graduate texts in mathematics. New York (NY): Springer; 2009.
  • Ikehata M. A special green’s function for the biharmonic operator and its application to an inverse boundary value problem. Comput. Math. Appl. 1991;22:53–66.
  • Isakov V. Completeness of products of solutions and some inverse problems for PDE. J. Differ. Equ. 1991;92:305–316.
  • Krupchyk K, Lassas M, Uhlmann G. Determining a first order perturbation of the biharmonic operator by partial boundary measurements. J. Funct. Anal. 2012;262:1781–1801.
  • Krupchyk K, Lassas M, Uhlmann G. Inverse boundary value problems for the perturbed polyharmonic operator. Trans. Amer. Math. Soc. 2014;1:95–112.
  • Yang Y. Determining the first order perturbation of a bi-harmonic operator on bounded and unbounded domains from partial data. J. Differ. Equ. 2014;257:3607–3639.
  • Ashbaugh MS. On universal inequalities for the low eigenvalues of the buckling problem. In: Carlos C, Raúl M, Gunther U, Michael SV, editors. Partial differential equations and inverse problems. Vol. 362, Contemporary Mathematics. Providence (RI): American Mathematical Society; 2004. p. 13–31.
  • Gazzola F, Grunau H-C, Sweers G. Polyharmonic boundary value problems. In: Morel J-M, Teissier B, De Lellis C, di Bernardo M, Figalli A, Khoshnevisan D, Kontoyiannis I, Lugosi G, Podolskij M, Serfaty S, Stroppel C, Wienhard A, editors. Positivity preserving and nonlinear higher order elliptic equations in bounded domains. Vol. 1991, Lecture notes in mathematics. Berlin: Springer-Verlag; 2010. p. xviii+423.
  • Ventsel E, Krauthammer T. Thin plates and shells: theory: analysis, and applications. New York: CRC Press; 2001.
  • Bukhgeim A, Uhlmann G. Recovering a potential from Cauchy data. Commun. Partial Differ. Equ. 2007;27:653–688.
  • Calderón A-P. On an inverse boundary value problem. In: Meyer WH, Raupp MA, editors. Seminar on numerical analysis and its applications to continuum physics (Rio de Janeiro, 1980). Rio de Janeiro: Sociedade Brasileira de Matemática; 1980. p. 65–73.
  • Ferreira DDS, et al. Determining a magnetic Schrödinger operator from partial Cauchy data. Commun. Math. Phys. 2007;2:467–488.
  • Kenig C, Sjöstrand J, Uhlmann G. The calderón’s problem with partial data. Ann. Math. (2). 2007;165:567–591.
  • Sylvester J, Uhlmann G. A global uniqueness theorem for an inverse boundary value problem. Ann. Math. (2). 1987;125:152–169.
  • Salo M, Tzou L. Carleman estimates and inverse problems for dirac operators. Math. Ann. (1). 2009;344:161–184.

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.