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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)

##### MSC:
 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