Linearized Calderón problem and exponentially accurate quasimodes for analytic manifolds
Krupchyk, K., Liimatainen, T., & Salo, M. (2022). Linearized Calderón problem and exponentially accurate quasimodes for analytic manifolds. Advances in Mathematics, 403, Article 108362. https://doi.org/10.1016/j.aim.2022.108362
Published inAdvances in Mathematics
DisciplineMatematiikkaInversio-ongelmien huippuyksikköMathematicsCentre of Excellence in Inverse Problems
© 2022 the Authors
In this article we study the linearized anisotropic Calderón problem on a compact Riemannian manifold with boundary. This problem amounts to showing that products of pairs of harmonic functions of the manifold form a complete set. We assume that the manifold is transversally anisotropic and that the transversal manifold is real analytic and satisfies a geometric condition related to the geometry of pairs of intersecting geodesics. In this case, we solve the linearized anisotropic Calderón problem. The geometric condition does not involve the injectivity of the geodesic X-ray transform. Crucial ingredients in the proof of our result are the construction of Gaussian beam quasimodes on the transversal manifold, with exponentially small errors, as well as the FBI transform characterization of the analytic wave front set.
ISSN Search the Publication Forum0001-8708
Publication in research information system
MetadataShow full item record
Showing items with similar title or keywords.
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 ...
Limiting Carleman weights and conformally transversally anisotropic manifolds Angulo, Pablo; Faraco, Daniel; Guijarro, Luis; Salo, Mikko (American Mathematical Society, 2020)We analyze the structure of the set of limiting Carleman weights in all conformally flat manifolds, $ 3$-manifolds, and $ 4$-manifolds. In particular we give a new proof of the classification of Euclidean limiting Carleman ...
Refined instability estimates for some inverse problems Kow, Pu-Zhao; Wang, Jenn-Nan (American Institute of Mathematical Sciences (AIMS), 2022)Many inverse problems are known to be ill-posed. The ill-posedness can be manifested by an instability estimate of exponential type, first derived by Mandache . In this work, based on Mandache's idea, we refine the ...
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 ...
Calderón's problem for p-laplace type equations Brander, Tommi (University of Jyväskylä, 2016)We investigate a generalization of Calderón’s problem of recovering the conductivity coeﬃcient in a conductivity equation from boundary measurements. As a model equation we consider the p-conductivity equation div σ ...