Identification of the curve of discontinuity of the determinant of the anisotropic conductivity
Masaru Ikehata · Journal of Inverse and Ill-Posed Problems · 2000
Abstract - Consider an anisotropic conductor of electric current which occupies a domain Ω ⊂ℝ2 with conductivity coefficient A = A0 +BχD, where D is a subdomain of Ω, A0 and A0+B are real, symmetric, uniformly positive definite and 2×2-matrix-valued functions. Denote by ΛA(f) the flux across ∂Ω induced by an electric potential f on ∂Ω. We prove that D can be uniquely determined by ΛA(f) for infinitely many f provided det A is discontinuous on ∂D and B is small on ∂D.