zbMATH — the first resource for mathematics

Inverse problems for nonsmooth first order perturbations of the Laplacian. (English) Zbl 1059.35175
Annales Academiæ Scientiarum Fennicæ. Mathematica. Dissertationes 139. Helsinki: Suomalainen Tiedeakatemia. Helsinki: Univ. of Helsinki, Department of Mathematics and Statistics (Thesis) (ISBN 951-41-0934-1/pbk). 67 p. (2004).
This manuscript concerns the study of the Dirichlet to Neumann map for solving inverse coefficient identification problems. The basic ideas are the reduction of a smooth elliptic equation into a Schrödinger equation and a perturbation argument. All the analysis applies for the dimension \(n\geq 3\) since complex geometrical solutions are employed. Between other uniqueness results we mention, notably, that for Lipschitz bounded domains, the Dirichlet to Neumann map determines uniquely a Lipschitz fluid velocity field in the convection-diffusion equation.
Reviewer: D. Lesnic (Leeds)

35R30 Inverse problems for PDEs
35J10 Schrödinger operator, Schrödinger equation
35J25 Boundary value problems for second-order elliptic equations
35Q40 PDEs in connection with quantum mechanics