CORRIGENDUM TO: “DUALITY BETWEEN RANGE AND NO-RESPONSE TESTS AND ITS APPLICATION FOR INVERSE PROBLEMS” (Inverse Problems and Imaging, 15 (2021),367-386)

In the proof of Proposition A.2 of Appendix in our published paper [1], we used the continuity of the normal derivative of q(x) at @G. This is not true because q(x) is not a double layer potential. A correct proof can be given as follows: Let R(') = 0 with ' 2 H 1=2(@G). Then z = S['] satisfies (Formula Presented). By the unique continuation property of solutions of the Laplace equation, we have S['] = z = 0 on @G. Then by the bijectivity of S : H^-1,2(@G) ! H^-1,2(@G) given in Proposition A.1, we have ' = 0, which proves the injectivity of R.