Wrong papers in mathematics I. Paper by Cakoni F., Colton D., Monk P. in "Inverse Problems" and subsequent papers

Abstract

The long series of mistaken papers published in the mathematical journals with very high impact factor during 11 years is discussed. The following journals published these mistaken papers: Inverse Problems (1), Nonlinear Analysis (1), Boundary Value Problems (1), Journal of Differential Equations (1), Journal of Mathematical Physiscs (2), Mathematical Methods in the Applied Sciences (2). The number in brackets shows the number of published wrong papers involved in the discussion. This series of wrong papers has been generated by a mistake in the paper: Cakoni F., Colton D. and Monk P. The direct and inverse scattering problems for partially coated obstacles.

On mistaken papers by Gouzheng Yan et al and related papers, and on a paper by Weibing Wang and Xuxin Yang

“…Theorem 2.3 and Theorem 2.5 on solvability of certain boundary value problems are not proved also because they use Lemma 2.4. Detailed discussion is presented in where mistakes have been pointed out for the first time.…”

Corrigendum: The direct and inverse scattering problems for partially coated obstacles

“…There is an error in the proof of lemma 2.4 in [1] (pointed out in [2]). Specifically, in equation ( 29) of [1] we have incorrectly stated that the double layer operators K and K are adjoint with respect to the L 2 -inner product.…”