Stability estimates in inverse problems for the Schrödinger and wave equations with trapping

• Víctor Arnaiz ^[1] ; Colin Guillarmou ^[1]
  1. [1] University of Paris-Saclay

     University of Paris-Saclay

     Arrondissement de Palaiseau, Francia

     
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 39, Nº 2, 2023, págs. 495-538
• Idioma: inglés
• DOI: 10.4171/RMI/1327
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• Resumen

  • For a class of Riemannian manifolds with boundary that includes all negatively curved manifolds with strictly convex boundary, we establish Hölder type stability estimates in the geometric inverse problem of determining the electric potential or the conformal factor from the Dirichlet-to-Neumann map associated with the Schrödinger equation and the wave equation. The novelty in this result lies in the fact that we allow some geodesics to be trapped inside the manifold and have infinite length.