Determining an unbounded potential from Cauchy data in admissible geometries
| Autor: | Carlos E. Kenig, Mikko Salo, David Dos Santos Ferreira |
|---|---|
| Přispěvatelé: | Institut Élie Cartan de Lorraine (IECL), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), Department of Mathematics, University of Chicago, Department of Mathematics and Statistics [Jyväskylä Univ] (JYU), University of Jyväskylä (JYU) |
| Jazyk: | angličtina |
| Rok vydání: | 2013 |
| Předmět: |
Mathematics::Analysis of PDEs
Boundary (topology) Calderón inverse problem 01 natural sciences Mathematics - Analysis of PDEs Spectral cluster FOS: Mathematics [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP] 0101 mathematics Anisotropy Mathematics Applied Mathematics 010102 general mathematics Mathematical analysis ta111 Cauchy distribution Inverse problem Mathematics::Spectral Theory Attenuated geodesic ray transform Carleman estimates 010101 applied mathematics Product (mathematics) Mathematics::Differential Geometry Complex geometrical optics Analysis Analysis of PDEs (math.AP) |
| Zdroj: | Communications in Partial Differential Equations Communications in Partial Differential Equations, Taylor & Francis, 2013, 38 (1), pp.50-68. ⟨10.1080/03605302.2012.736911⟩ |
| ISSN: | 0360-5302 1532-4133 |
| DOI: | 10.1080/03605302.2012.736911⟩ |
| Popis: | In [4 Dos Santos Ferreira , D. , Kenig , C.E. , Salo , M. , Uhlmann , G. ( 2009 ). Limiting Carleman weights and anisotropic inverse problems . Invent. Math. 178 : 119 – 171 . [Crossref], [Web of Science ®], [Google Scholar] ] anisotropic inverse problems were considered in certain admissible geometries, that is, on compact Riemannian manifolds with boundary which are conformally embedded in a product of the Euclidean line and a simple manifold. In particular, it was proved that a bounded smooth potential in a Schrödinger equation was uniquely determined by the Dirichlet-to-Neumann map in dimensions n ≥ 3. In this article we extend this result to the case of unbounded potentials, namely those in L n/2. In the process, we derive L p Carleman estimates with limiting Carleman weights similar to the Euclidean estimates of Jerison and Kenig [8 Jerison , D. , Kenig , C.E. ( 1985 ). Unique continuation and absence of positive eigenvalues for Schrödinger operators . Ann. Math. 121 : 463 – 494 . [Crossref], [Web of Science ®], [Google Scholar] ] and Kenig et al. [9 Kenig , C.E. , Ruiz , A. , Sogge , C.D. ( 1987 ). Uniform Sobolev inequalities and unique continuation for second order constant coefficient differential operators . Duke Math. J. 55 : 329 – 347 . [Crossref], [Web of Science ®], [Google Scholar] ]. peerReviewed |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|