Determining a Magnetic Schrödinger Operator from Partial Cauchy Data

By David dos Santos Ferreira, Carlos E. Kenig, J. Sjöstrand, Gunther Uhlmann. 2006

187 citations recorded by the source corpus.

In this paper we show, in dimension n ≥ 3, that knowledge of the Cauchy data for the Schrödinger equation in the presence of a magnetic potential, measured on possibly very small subsets of the boundary, determines uniquely the magnetic field and the electric potential. We follow the general strategy of [7] using a richer set of solutions to the Dirichlet problem that has been used in previous works on this problem.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/e797cc628ec32d9ab933123e53ff69dfdc7cfff9

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In Applied Mathematics

In Computational Theory and Mathematics

In Mathematical Physics

Citations in the corpus

The Calderón problem with partial data on manifolds and applications (2012, result): “Based on this approach, there are low regularity results [Knudsen 2006; Zhang 2012], results for other scalar equations [Ferreira 2007; Knudsen and Salo 2007; Chung 2012] and systems [Salo and Tzou 2010; Chung et al.”
Limiting Carleman weights and anisotropic inverse problems (2008, methodology): “The present proof makes it possible to include boundary terms, which is useful in the study of inverse problems with partial data (see [13], [7] and [14]).”
Determining the first order perturbation of a bi-harmonic operator on bounded and unbounded domains from partial data (2013, background): “For the construction of various CGO solutions and their application, see [1, 2, 3, 4, 14, 17].”
The Calderón problem with partial data in two dimensions (2010, background): “The case of the magnetic Schrödinger equation was considered in [11] and an improvement on the regularity of the coefficients is done in [21].”
GLOBAL UNIQUENESS FOR THE CALDERÓN PROBLEM WITH LIPSCHITZ CONDUCTIVITIES (2014, unknown): “Recalling that (−∆+ 2ζ · ∇ + q) = e ·ζ (−∆+ q)e ·ζ , in order to remove the smallness condition, we introduce convex Carleman weights in the spirit of [16], [9] or [18].”
Partial Cauchy data for general second order elliptic operators in two dimensions (2010, methodology): “The same is valid for the case of partial Cauchy data [10].”
REGULARIZED D-BAR METHOD FOR THE INVERSE CONDUCTIVITY PROBLEM (2009, background): “For recent development on new kinds of cgo solutions for inverse problems, see [16, 20, 47, 55].”
Electrical impedance tomography and Calderón's problem (2009, methodology): “We review the recent construction of complex geometrical optics construction for a class of Riemannian manifolds based on [30].”