Partial data inverse problems for quasilinear conductivity equations

Increasing stability of a linearized inverse boundary value problem for a nonlinear Schrödinger equation on transversally anisotropic manifolds

“…The study on inverse boundary value problems for nonlinear elliptic equations goes back to [18,28,29]. For more recent works, we refer to [2,6,21,20,5,10] and the references therein.…”

Lipschitz and Hölder stable determination of nonlinear terms for elliptic equations

“…In the more recent works [9,21], the authors addressed the stability issue for this last problem for quasilinear terms depending only on the solution from some restriction of the Dirichlet-to-Neumann map associated with (1.3). Similar problems have been investigated for more general class of quasilinear terms depending also on the space variable in the works [5,6,22,31,32] among which the most general one can be found in [6] where the authors addressed the open problem of determining quasilinear terms depending simultaneously on the solutions, the gradient of the solutions and the space variable. Finally, we mention the works [13,17,19,20,24,25,27] devoted to the determination of semilinear terms by using the first order linearization technique of [18] as well as the higher order linearization initiated by [26].…”

Stable determination of the nonlinear term in a quasilinear elliptic equation by boundary measurements

“…We refer to the recent work [2] and references therein for more details. We also quote without being exhaustive the following references [1,5,6,9,10,12,14,15,16,17,18,19,20,21] on semilinear and quasilinear elliptic inverse problems.…”