Quantitative Runge Approximation and Inverse Problems
Rüland, A., & Salo, M. (2019). Quantitative Runge Approximation and Inverse Problems. International Mathematics Research Notices, 2019(20), 6216-6234. https://doi.org/10.1093/imrn/rnx301
Published in
International Mathematics Research NoticesDate
2019Copyright
© 2018 Oxford University Press
In this short note, we provide a quantitative version of the classical Runge approximation property for second-order elliptic operators. This relies on quantitative unique continuation results and duality arguments. We show that these estimates are essentially optimal. As a model application, we provide a new proof of the result from [8], [2] on stability for the Calderón problem with local data.
Publisher
Oxford University PressISSN Search the Publication Forum
1073-7928Keywords
Publication in research information system
https://converis.jyu.fi/converis/portal/detail/Publication/27840396
Metadata
Show full item recordCollections
Related funder(s)
Academy of Finland; European CommissionFunding program(s)
Centre of Excellence, AoF; FP7 (EU's 7th Framework Programme)

The content of the publication reflects only the author’s view. The funder is not responsible for any use that may be made of the information it contains.
Additional information about funding
A.R. gratefully acknowledges a Junior Research Fellowship at Christ Church. M.S. was supported by the Academy of Finland (Finnish Centre of Excellence in Inverse Problems Research, grant number 284715) and an ERC Starting Grant (grant number 307023).License
Related items
Showing items with similar title or keywords.
-
Inverse problems for elliptic equations with power type nonlinearities
Lassas, Matti; Liimatainen, Tony; Lin, Yi-Hsuan; Salo, Mikko (Elsevier, 2021)We introduce a method for solving Calderón type inverse problems for semilinear equations with power type nonlinearities. The method is based on higher order linearizations, and it allows one to solve inverse problems for ... -
Applications of Microlocal Analysis in Inverse Problems
Salo, Mikko (MDPI AG, 2020)This note reviews certain classical applications of microlocal analysis in inverse problems. The text is based on lecture notes for a postgraduate level minicourse on applications of microlocal analysis in inverse problems, ... -
The Calderón problem for the fractional Schrödinger equation
Ghosh, Tuhin; Salo, Mikko; Uhlmann, Gunther (Mathematical Sciences Publishers, 2020)We show global uniqueness in an inverse problem for the fractional Schrödinger equation: an unknown potential in a bounded domain is uniquely determined by exterior measurements of solutions. We also show global uniqueness ... -
The Fixed Angle Scattering Problem with a First-Order Perturbation
Meroño, Cristóbal J.; Potenciano-Machado, Leyter; Salo, Mikko (Springer Science and Business Media LLC, 2021)We study the inverse scattering problem of determining a magnetic field and electric potential from scattering measurements corresponding to finitely many plane waves. The main result shows that the coefficients are uniquely ... -
Unique continuation property and Poincaré inequality for higher order fractional Laplacians with applications in inverse problems
Covi, Giovanni; Mönkkönen, Keijo; Railo, Jesse (American Institute of Mathematical Sciences (AIMS), 2021)We prove a unique continuation property for the fractional Laplacian (−Δ)s when s∈(−n/2,∞)∖Z where n≥1. In addition, we study Poincaré-type inequalities for the operator (−Δ)s when s≥0. We apply the results to show that ...