Abbreviated Journal Title
SIAM J. Math. Anal.
Calderon problem; frequency differential electrical impedance; tomography; complex geometrical optics; BOUNDARY-VALUE PROBLEM; GLOBAL UNIQUENESS; FEASIBILITY; Mathematics, Applied
Recent research in electrical impedance tomography produced images of biological tissue from frequency differential boundary voltages and corresponding currents. Physically one is to recover the electrical conductivity sigma and permittivity c from the frequency differential boundary data. Let gamma = sigma+iota omega is an element of denote the complex admittivity, Lambda(gamma) be the corresponding Dirichlet-to-Neumann map, and d Lambda(gamma)/d omega|omega=0 be its frequency differential at omega = 0. If sigma is an element of C-1,C-1 ((Omega) over bar) is constant near the boundary and is an element of is an element of C-0(1,1) (Omega), we show that d Lambda(gamma)/d omega|omega=0 uniquely determines del center dot (del is an element of - is an element of del ln sigma)/sigma inside Omega. In addition, if Lambda(gamma)|(omega=0) is also known, then is an element of and sigma can be reconstructed inside. The method of proof uses the complex geometrical optics solutions.
Siam Journal on Mathematical Analysis
Kim, Sungwhan and Tamasan, Alexandru, "On A Calderon Problem In Frequency Differential Electrical Impedance Tomography" (2013). Faculty Bibliography 2010s. 4210.