Determining an Unbounded Potential from Cauchy Data in Admissible Geometries

By David dos Santos Ferreira, Carlos E. Kenig, Mikko Salo. 2011

61 citations recorded by the source corpus.

In [4] 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] and Kenig et al. [9].

Subfields: Computational Theory and Mathematics, Mathematical Physics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/7cdd73350c3bba4c1ad9771375cb8a7edb51ec75

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In Computational Theory and Mathematics

  1. Mikko Salo
  2. Yaroslav Kurylev
  3. Matti Lassas
  4. David dos Santos Ferreira
  5. Gunther Uhlmann
  6. Katya Krupchyk
  7. Lauri Oksanen
  8. Masahiro Yamamoto

In Mathematical Physics

  1. Mikko Salo
  2. Gunther Uhlmann
  3. Matti Lassas
  4. Yaroslav Kurylev
  5. David dos Santos Ferreira
  6. Carlos E. Kenig
  7. Lauri Oksanen
  8. Katya Krupchyk

In Mechanics of Materials

  1. Matti Lassas
  2. Yaroslav Kurylev
  3. Mikko Salo
  4. David dos Santos Ferreira
  5. Gunther Uhlmann
  6. Lauri Oksanen

Citations in the corpus