Runge approximation and stability improvement for a partial data Calderón problem for the acoustic Helmholtz equation
| Autor: | Angkana Rüland, Wiktoria Zatoń, María Ángeles García-Ferrero |
|---|---|
| Jazyk: | angličtina |
| Předmět: |
Control and Optimization
Helmholtz equation Function space 010102 general mathematics Mathematical analysis Regular polygon Contrast (statistics) Inverse problem 01 natural sciences Stability (probability) 010101 applied mathematics Continuation Mathematics - Analysis of PDEs Modeling and Simulation FOS: Mathematics Discrete Mathematics and Combinatorics Pharmacology (medical) Limit (mathematics) 0101 mathematics Analysis Analysis of PDEs (math.AP) Mathematics |
| Zdroj: | Inverse problems and imaging |
| ISSN: | 1930-8345 1930-8337 |
| DOI: | 10.3934/ipi.2021049 |
| Popis: | 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. Comment: 28 pages, comments welcome |
| Databáze: | OpenAIRE |
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