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SEMILINEAR CALDERÓN PROBLEM ON STEIN MANIFOLDS WITH KÄHLER METRIC

Part of: Miscellaneous topics - Partial differential equations

Published online by Cambridge University Press:  20 May 2020

YILIN MA Open the ORCID record for YILIN MA [Opens in a new window]  and
LEO TZOU Open the ORCID record for LEO TZOU [Opens in a new window]
YILIN MA*
Affiliation:
School of Mathematics and Statistics,The University of Sydney, Camperdown, New South Wales 2006, Australia email K.Ma@maths.usyd.edu.au
LEO TZOU
Affiliation:
School of Mathematics and Statistics,The University of Sydney, Camperdown, New South Wales 2006, Australia email leo.tzou@sydney.edu.au
*
✉K.Ma@maths.usyd.edu.au
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Abstract

We extend existing methods which treat the semilinear Calderón problem on a bounded domain to a class of complex manifolds with Kähler metric. Given two semilinear Schrödinger operators with the same Dirchlet-to-Neumann data, we show that the integral identities that appear naturally in the determination of the analytic potentials are enough to deduce uniqueness on the boundary up to infinite order. By exploiting the assumed complex structure, this information allows us to apply the method of stationary phase and recover the potentials in the interior as well.

Keywords

nonlinear inverse problemspartial dataCalderón problem

MSC classification

Primary: 35R30: Inverse problems
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 103 , Issue 1 , February 2021 , pp. 132 - 144
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Copyright
© 2020 Australian Mathematical Publishing Association Inc.

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