Parameter identification for elliptic problems

The problem of computing a principal coefficient function P in the differential equation −∇·(P(x)∇u)=f, x∈Ω⊂RM, M⩾1, on a bounded region Ω from a knowledge of the solution function u and the right-hand side f, where u, f are known only approximately and P may have mild discontinuities, is solved by minimization of an associated functional.