Total determination of material parameters from electromagnetic boundary information

Boundary integral formulae for the reconstruction of electric and electromagnetic inhomogeneities of small volume

“…To summarize: we have at this point at our disposal two asymptotic formulae with which to reconstruct the inhomogeneities; if the inhomogeneities are all of small diameter, then 13) and if the inhomogeneities are all thin strips (in two dimensions) then…”

Geometric Methods for Anisotopic Inverse Boundary Value Problems

“…In the scalar case there is a factorisation modulo smoothing operators ∆ The proof given in [8] differs from Lee and Uhlmann's is in its use of families of operators parameterized by the normal distance x n . This technique was also used by Joshi and McDowall [10] with P j a smooth family of operators on Y of order m¨j. This definition extends naturally to operators on bundles, in our case the bundle of k-forms being the important example.…”

Partial data inverse problems for Maxwell equations via Carleman estimates

“…Earlier results include [SIC92,SU92,CP92], and a simplified proof was presented in [OS96]. Stability results for this inverse problem are in [Ca10,Ca11], boundary determination results are in [Mc97,JM00], the case of chiral media is considered in [Mc00], and a recent uniqueness result for C 1 coefficients is given in [CZ13]. The inverse problem for Maxwell equations on manifolds was discussed in [OPS03].…”