Bukhgeim, Alexander L.; Uhlmann, Gunther Recovering a potential from partial Cauchy data. (English) Zbl 0998.35063 Commun. Partial Differ. Equations 27, No. 3-4, 653-668 (2002). Summary: We prove in dimension \(n\geq 3\) that knowledge of the Cauchy data for the Schrödinger equation measured on particular subsets of the boundary determines uniquely the potential. Cited in 4 ReviewsCited in 106 Documents MSC: 35R30 Inverse problems for PDEs 35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation Keywords:Helmholtz equation; Dirichlet-to-Neumann map; Carleman estimates; uniqueness; Cauchy data; Schrödinger equation × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Dautray, Mathematical Analysis and Numerical Methods for Science and Technology 2 (1993) · Zbl 0802.35001 [2] Greenleaf G., to Appear Duke Math. J. [3] Kohn R., Comm. Pure Appl. Math. 37 pp 289– (1984) · Zbl 0586.35089 · doi:10.1002/cpa.3160370302 [4] Lions J.-L., Problemes aux Limites Non Homogenes et Applications 1 (1970) · Zbl 0197.06701 [5] Nachman A.I., Ann. of Math. 143 pp 71– (1996) · Zbl 0857.35135 · doi:10.2307/2118653 [6] Sylvester J., Ann. of Math. 125 pp 153– (1987) · Zbl 0625.35078 · doi:10.2307/1971291 [7] Sun Z.Q., Duke Math. J. 62 pp 131– (1991) · Zbl 0728.35132 · doi:10.1215/S0012-7094-91-06206-X [8] Sun Z.Q., Comm. Math. Phys. 153 pp 431– (1993) · Zbl 0795.35142 · doi:10.1007/BF02096948 [9] Taylor M., Partial Differential Equations 1 (1996) · Zbl 0869.35001 · doi:10.1007/978-1-4684-9320-7 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.