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

Eemeli  Blåsten; Oleg Yu. Imanuvilov; Masahiro Yamamoto

doi:10.3934/ipi.2015.9.709

Article Contents

2015, Volume 9, Issue 3: 709-723. Doi: 10.3934/ipi.2015.9.709

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

1.
Department of Mathematics, Tallinn University of Technology, Ehitajate tee 5, 19086 Tallinn
2.
Department of Mathematics, Colorado State University,101 Weber Building, Fort Colins, CO 80523-1784
3.
Department of Mathematical Sciences, The University of Tokyo, Komaba Meguro Tokyo 153-8914

Received: September 30, 2014

Revised: January 31, 2015

Published: July 2015

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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 $p>2$.

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Mathematics Subject Classification: Primary: 35R30, 30G20; Secondary: 35J10.

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