Convergence rates for Tikhonov regularization of coefficient identification problems in Laplace-type equations

We investigate the convergence rates for Tikhonov regularization of the problem of identifying (1) the coefficient q ∈ L ∈fty(Ω) in the Dirichlet problem −div(q∇u) = f in Ω, u = 0 on ∂Ω, and (2) the coefficient a in Linfty(Ω) in the Dirichlet problem −Δu + au = f in Ω, u = 0 on ∂Ω, when u is imprecisely given by zδ in H10(Ω), ∥u-zδ∥H1(Ω) ≤ δ, Ω ⊂ Rd, d ≥ 1. Further, we give very simple source conditions without the smallness requirement on the source functions which provide the convergence rate O(√(δ)) for the regularized solutions