An inverse resistivity problem: 1. Lipschitz continuity of the gradient of the objective functional

摘要

A mathematical model of vertical electrical sounding over a medium with continuously changing conductivity σ(z) is studied by using a resistivity method. The considered model leads to an inverse problem of identification of the unknown leading coefficient σ(z) of the elliptic equation {partial deriv}/{partial deriv}z(σ(z){partial deriv}u/{partial deriv}z) + σ(z)/r{partial deriv}/{partial deriv}r(r {partial deriv}u/{partial deriv}r)=0 in the layer Ω={(r, z) ∈ R~2: 0≤r<∞, 0