Open AccessRunge approximation and stability improvement for a partial data Calderón problem for the acoustic Helmholtz equation
Author(s) -
María Ángeles García-Ferrero,
Angkana Rüland,
Wiktoria Zatoń
Publication year - 2022
Publication title -
inverse problems and imaging
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.755
H-Index - 40
eISSN - 1930-8345
pISSN - 1930-8337
DOI - 10.3934/ipi.2021049
Subject(s) - mathematics , stability (learning theory) , helmholtz equation , regular polygon , helmholtz free energy , mathematical analysis , inverse , continuation , function (biology) , convex function , physics , geometry , computer science , thermodynamics , machine learning , evolutionary biology , biology , programming language , boundary value problem
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.