Calderón uniqueness for bounded measurable real isotropic conductivities

For every integer n>=3, every bounded connected Lipschitz domain Omega in R^n and every pair of real scalar conductivities gamma_1,gamma_2 in L-infinity(Omega) with 0<c<=gamma_j<=C<infinity almost everywhere for some constants c,C, equality Lambda_gamma_1=Lambda_gamma_2 of the full weak Dirichlet-to-Neumann operators H^(1/2)(boundary Omega)->H^(-1/2)(boundary Omega) implies gamma_1=gamma_2 almost everywhere. For trace f, u is the unique H^1 solution of div(gamma grad u)=0 with trace f, and <Lambda_gamma f,g>=integral_Omega gamma grad u dot grad v for any H^1 extension v of test trace g. No coefficient derivatives, boundary agreement, connected-complement, smallness or nonzero-frequency hypothesis is imposed.

Source: Matteo Santacesaria, Note on Calderón's inverse problem for measurable conductivities, Inverse Problems and Imaging13(1)(2019),149–157; arXiv1803.06931v2.

Status Open · subcases solved Status review date not recorded in this edition

Listed by ProofAtlas. Status qualification is attributed to ProofAtlas; no full resolution is certified here.