Runge Approximation and Stability Improvement for a Partial Data Calder\'on Problem for the Acoustic Helmholtz Equation
Analysis of PDEs
2021-01-12 v1
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 \cite{AU04, KU19}. 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.
Cite
@article{arxiv.2101.04089,
title = {Runge Approximation and Stability Improvement for a Partial Data Calder\'on Problem for the Acoustic Helmholtz Equation},
author = {María Ángeles García-Ferrero and Angkana Rüland and Wiktoria Zatoń},
journal= {arXiv preprint arXiv:2101.04089},
year = {2021}
}
Comments
28 pages, comments welcome