Balgaisha Mukanova An inverse resistivity problem: 1. Frechet differentiability of the cost functional and Lipschitz continuity of the gradient (285K, .pdf) ABSTRACT. Mathematical model of vertical electrical sounding (VES) over a medium with continuously changing conductivity $\sigma(z)$ is studied by using a resistivity method. The considered model leads to an inverse problem of identification of the unknown leading coefficient $\sigma(z)$ of the elliptic equation $\frac{\partial}{\partial z}(\sigma(z)\frac{\partial u}{\partial z})+\frac{\sigma(z)}{r}\frac{\partial}{\partial r}(r \frac{\partial u}{\partial r})=0$ in the layer $\Omega=\{(r,z)\in R^2:~0\leq r<\infty,~ 0