Inverse Problems and Imaging (IPI)

Stability and uniqueness for a two-dimensional inverse boundary value problem for less regular potentials

Pages: 709 - 723, Volume 9, Issue 3, August 2015      doi:10.3934/ipi.2015.9.709

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Eemeli Blåsten - Department of Mathematics, Tallinn University of Technology, Ehitajate tee 5, 19086 Tallinn, Estonia (email)
Oleg Yu. Imanuvilov - Department of Mathematics, Colorado State University,101 Weber Building, Fort Colins, CO 80523-1784, United States (email)
Masahiro Yamamoto - Department of Mathematical Sciences, The University of Tokyo, Komaba Meguro Tokyo 153-8914, Japan (email)

Abstract: We consider inverse boundary value problems for the Schrödinger equations in two dimensions. Within less regular classes of potentials, we establish a conditional stability estimate of logarithmic order. Moreover we prove the uniqueness within $L^p$-class of potentials with $p>2$.

Keywords:  Calderón problem, stability, uniqueness.
Mathematics Subject Classification:  Primary: 35R30, 30G20; Secondary: 35J10.

Received: October 2014;      Revised: February 2015;      Available Online: July 2015.