Fractional anisotropic Calderón problem on complete Riemannian manifolds

2023/03/07 by Choulli, Mourad, Ouhabaz, El Maati
#35R01 #35R11 #35R30 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2303.03764

Abstract

We prove that the metric tensor g of a complete Riemannian manifold is uniquely determined, up to isometry, from the knowledge of a local source-to-solution operator. This later is associated to a fractional power of the Laplace-Belrami operator Δ_g. Our result holds under the condition that the metric tensor g is known in an arbitrary small subdomain. We also consider the case of closed manifolds and provide an improvement of the main result in \citeFGKU

Related

• Fractional anisotropic Calderón problem on closed Riemannian manifolds
• Fractional anisotropic Calderón problem with external data
• On the anisotropic Calderón's problem
• The fractional anisotropic Calderón problem for a nonlocal parabolic equation on closed Riemannian manifolds
• Calderón problem for fractional Schrödinger operators on closed Riemannian manifolds