The Linearized Calderón Problem in Transversally Anisotropic Geometries
| Autor: | David Dos Santos Ferreira, Tony Liimatainen, Mikko Salo, Matti Lassas, Yaroslav Kurylev |
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| Přispěvatelé: | Department of Mathematics and Statistics, Inverse Problems, Matti Lassas / Principal Investigator |
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Mathematics - Differential Geometry
Geodesic General Mathematics NEUMANN MAP Boundary (topology) Type (model theory) 01 natural sciences law.invention Mathematics - Analysis of PDEs linearized anisotropic Calderón problem law 35R30 35J25 111 Mathematics FOS: Mathematics 0101 mathematics Mathematics 010102 general mathematics Mathematical analysis Inverse problem 010101 applied mathematics Harmonic function Differential Geometry (math.DG) Transversal (combinatorics) Gravitational singularity Mathematics::Differential Geometry INVERSE PROBLEM Manifold (fluid mechanics) Analysis of PDEs (math.AP) |
| Popis: | In this article we study the linearized anisotropic Calderon problem. In a compact manifold with boundary, this problem amounts to showing that products of harmonic functions form a complete set. Assuming that the manifold is transversally anisotropic, we show that the boundary measurements determine an FBI type transform at certain points in the transversal manifold. This leads to recovery of transversal singularities in the linearized problem. The method requires a geometric condition on the transversal manifold related to pairs of intersecting geodesics, but it does not involve the geodesic X-ray transform which has limited earlier results on this problem. Comment: 27 pages |
| Databáze: | OpenAIRE |
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