Revista Matemática Iberoamericana


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Published online first: 2019-10-14
DOI: 10.4171/rmi/1143

Determination of non-compactly supported electromagnetic potentials in an unbounded closed waveguide

Yavar Kian[1]

(1) Aix-Marseille Université, Marseille, France

We study the inverse problem of determining a magnetic Schrödinger operator in an unbounded closed waveguide from boundary measurements. We consider this problem with a general closed waveguide in the sense that we only require our unbounded domain to be contained into an infinite cylinder. In this context we prove the unique recovery of the magnetic field and the electric potential associated with general bounded and non-compactly supported electromagnetic potentials. By assuming that the electromagnetic potentials are known on the neighborhood of the boundary outside a compact set, we even prove the unique determination of the magnetic field and the electric potential from measurements restricted to a bounded subset of the infinite boundary. Finally, in the case of a waveguide taking the form of an infinite cylindrical domain, we prove the recovery of the magnetic field and the electric potential from partial data corresponding to restriction of Neumann boundary measurements to slightly more than half of the boundary. We establish all these results by mean of a new class of complex geometric optics solutions and of Carleman estimates suitably designed for our problem stated in an unbounded domain and with bounded electromagnetic potentials.

Keywords: Inverse problems, elliptic equations, electromagnetic potential, Carleman estimate, unbounded domain, closed waveguide, partial data

Kian Yavar: Determination of non-compactly supported electromagnetic potentials in an unbounded closed waveguide. Rev. Mat. Iberoam. Electronically published on October 14, 2019. doi: 10.4171/rmi/1143 (to appear in print)