We study the inverse boundary problem for a nonlinear magnetic Schrodinger operator on a conformally transversally anisotropic Riemannian manifold of dimension n >= 3. Under suitable assumptions on the nonlinearity, we show that the knowledge of the Dirichlet-to-Neumann map on the boundary of the manifold determines the nonlinear magnetic and electric potentials uniquely. No assumptions on the transversal manifold are made in this result, whereas the corresponding inverse boundary problem for the linear magnetic Schrodinger operator is still open in this generality.
机构:
Ecole Normale Super, UMR CNRS 8553, DMA, 45 Rue Ulm, F-75230 Paris 05, FranceEcole Normale Super, UMR CNRS 8553, DMA, 45 Rue Ulm, F-75230 Paris 05, France
机构:
Ecole Normale Super, UMR CNRS 8553, DMA, 45 Rue Ulm, F-75230 Paris 05, FranceEcole Normale Super, UMR CNRS 8553, DMA, 45 Rue Ulm, F-75230 Paris 05, France