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SEMILINEAR CALDERÓN PROBLEM ON STEIN MANIFOLDS WITH KÄHLER METRIC

Published online by Cambridge University Press:  20 May 2020

YILIN MA*
Affiliation:
School of Mathematics and Statistics,The University of Sydney, Camperdown, New South Wales 2006, Australia email [email protected]
LEO TZOU
Affiliation:
School of Mathematics and Statistics,The University of Sydney, Camperdown, New South Wales 2006, Australia email [email protected]

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.

MSC classification

Type
Research Article
Copyright
© 2020 Australian Mathematical Publishing Association Inc.

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