Li HJENN-NAN WANGWang L.2022-04-252022-04-25202219308337https://www.scopus.com/inward/record.uri?eid=2-s2.0-85123550534&doi=10.3934%2fipi.2021048&partnerID=40&md5=1ea126e67815c36664520e07e4f98257https://scholars.lib.ntu.edu.tw/handle/123456789/606441In this paper we study the inverse problem of determining an electrical inclusion in a multi-layer composite from boundary measurements in 2D. We assume the conductivities in different layers are different and derive a stability estimate for the linearized map with explicit formulae on the conductivity and the thickness of each layer. Intuitively, if an inclusion is surrounded by a highly conductive layer, then, in view of “the principle of the least work”, the current will take a path in the highly conductive layer and disregard the existence of the inclusion. Consequently, a worse stability of identifying the hidden inclusion is expected in this case. Our estimates indeed show that the ill-posedness of the problem increases as long as the conductivity of some layer becomes large. This work is an extension of the previous result by Nagayasu-Uhlmann-Wang[15], where a depth-dependent estimate is derived when an inclusion is deeply hidden in a conductor. Estimates in this work also show the influence of the depth of the inclusion. ? 2022, American Institute of Mathematical Sciences. All rights reserved.Calder?n’s problemConductivityDirichlet-to-Neumann mapEITMulti-layer com-positejournal article10.3934/ipi.20210482-s2.0-85123550534