Applications of Microlocal Analysis in Inverse Problems
Salo, M. (2020). Applications of Microlocal Analysis in Inverse Problems. Mathematics, 8(7), Article 1184. https://doi.org/10.3390/math8071184
Published in
MathematicsAuthors
Date
2020Discipline
MatematiikkaInversio-ongelmien huippuyksikköMathematicsCentre of Excellence in Inverse ProblemsCopyright
© 2020 by the author. Licensee MDPI, Basel, Switzerland.
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, given in Helsinki and Shanghai in June 2019.
Publisher
MDPI AGISSN Search the Publication Forum
2227-7390Keywords
Publication in research information system
https://converis.jyu.fi/converis/portal/detail/Publication/41624965
Metadata
Show full item recordCollections
Related funder(s)
European Commission; Academy of FinlandFunding program(s)
Academy Project, AoF; Centre of Excellence, AoF


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
The author was supported by the Academy of Finland (Finnish Centre of Excellence in Inverse Modelling and Imaging, grant numbers 312121 and 309963) and by the European Research Council under Horizon 2020 (ERC CoG 770924).License
Related items
Showing items with similar title or keywords.
-
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 ... -
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 ... -
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 Linearized Calderón Problem on Complex Manifolds
Guillarmou, Colin; Salo, Mikko; Tzou, Leo (Springer, 2019)In this note we show that on any compact subdomain of a K¨ahler manifold that admits sufficiently many global holomorphic functions, the products of harmonic functions form a complete set. This gives a positive answer to ... -
On some partial data Calderón type problems with mixed boundary conditions
Covi, Giovanni; Rüland, Angkana (Elsevier, 2021)In this article we consider the simultaneous recovery of bulk and boundary potentials in (degenerate) elliptic equations modelling (degenerate) conducting media with inaccessible boundaries. This connects local and nonlocal ...