Runge approximation and stability improvement for a partial data Calderón problem for the acoustic Helmholtz equation

María Ángeles García-Ferrero; Angkana Rüland; Wiktoria Zatoń

doi:10.3934/ipi.2021049

Article Contents

2022, Volume 16, Issue 1: 251-281. Doi: 10.3934/ipi.2021049

This issue Previous Article Refined stability estimates in electrical impedance tomography with multi-layer structure Next Article

Runge approximation and stability improvement for a partial data Calderón problem for the acoustic Helmholtz equation

1.
Institut für Angewandte Mathematik, Ruprecht-Karls-Universität Heidelberg, Im Neuenheimer Feld 205, 69120 Heidelberg, Germany
2.
Institut für Mathematik, Universität Zürich, Winterthurerstrasse 190, 8057 Zürich, Switzerland

^* Corresponding author: garciaferrero@uni-heidelberg.de
^* Corresponding author: garciaferrero@uni-heidelberg.de

Received: January 2021

Revised: May 2021

Early access: July 2021

Published: February 2022

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Abstract

In this article, we discuss quantitative Runge approximation properties for the acoustic Helmholtz equation and prove stability improvement results in the high frequency limit for an associated partial data inverse problem modelled on [3,35]. The results rely on quantitative unique continuation estimates in suitable function spaces with explicit frequency dependence. We contrast the frequency dependence of interior Runge approximation results from non-convex and convex sets.

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Mathematics Subject Classification: Primary: 35R30; Secondary: 35J05.

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