The Neumann problem for the 2‐D Helmholtz equation in a domain, bounded by closed and open curves

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

“…and H (1) 0 (z) is a Hankel function. However this assumption is wrong, the operator K is not adjoint to the operator K, and the relation (29) and the subsequent relation are mistaken.…”

The Neumann Problem in a 2-D Exterior Domain with Cuts and Singularities at the Tips

“…Another direction of the recent research [1,2,[4][5][6][7][11][12][13][14] It is very natural to join two kinds of the mentioned problems and to consider problems in domains with the boundary containing both closed and open surfaces [8][9][10]. Similar problems were not actively treated before even in the classical formulation for the 2-D harmonic functions.…”

The Neumann problem for the dissipative Helmholtz equation in the exterior of open Lipschitz surfaces

“…The 2D Neumann problem for the dissipative Helmholtz equation in both interior and exterior domains with cracks has been studied by boundary integral equation method in [14,15]. The 2D Neumann problem for the propagative Helmholtz equation in exterior domains with cracks has been analysed in [16][17][18].…”

“…The 2D Neumann problem for the propagative Helmholtz equation in exterior domains with cracks has been analysed in [16][17][18]. Problems in [14][15][16][17][18] have been reduced to the uniquely solvable integral equations. Uniqueness and existence of a classical solution have been proved in [14][15][16][17][18].…”

“…Problems in [14][15][16][17][18] have been reduced to the uniquely solvable integral equations. Uniqueness and existence of a classical solution have been proved in [14][15][16][17][18]. Integral representations for solutions have been obtained in [14][15][16][17][18] in the form of potentials.…”