We develop the $\overline{\partial }$-approach to inverse scattering at zero energy in dimensions $d\ge 3$ of [Beals, Coifman 1985], [Henkin, Novikov 1987] and [Novikov 2002]. As a result we give, in particular, uniqueness theorem, precise reconstruction procedure, stability estimate and approximate reconstruction for the problem of finding a sufficiently small potential $v$ in the Schrödinger equation from a fixed non-overdetermined (“backscattering” type) restriction ${h|}_{\Gamma }$ of the Faddeev generalized scattering amplitude $h$ in the...

Two problems arising in Environment are considered. The first one concerns a conjecture posed by von Neumann in 1955 on the possible modification of the albedo in order to control the Earth surface temperature. The second one is related to the approximate controllability of Stackelberg-Nash strategies for some optimization problems as, for instance, the pollution control in a lake. The results of the second part were obtained in collaboration with Jacques-Lois Lions.