Unique determination of the electric potential in the presence of a fixed magnetic potential in the plane

Caro, Pedro; Rogers, Keith M.

doi:10.5802/jedp.667

Caro, Pedro ¹ ; Rogers, Keith M.²

¹ BCAM - Basque Center for Applied Mathematics 48009 Bilbao Spain and Ikerbasque, Basque Foundation for Science 48011 Bilbao Spain
² Instituto de Ciencias Matemáticas CSIC-UAM-UC3M-UCM 28049 Madrid Spain

Journées équations aux dérivées partielles (2018), Exposé no. 7, 9 p. Cet article a éte moissonné depuis la source Numdam

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Résumé

For potentials $V \in L^{\infty} (ℝ^{2}, ℝ)$ and $A \in W^{1, \infty} (ℝ^{2}, ℝ^{2})$ with compact support, we consider the Schrödinger equation $- {(\nabla + i A)}^{2} u + V u = k^{2} u$ with fixed positive energy $k^{2}$ . Under a mild additional regularity hypothesis, and with fixed magnetic potential $A$ , we show that the scattering solutions uniquely determine the electric potential $V$ . For this we develop the method of Bukhgeim for the purely electric Schrödinger equation.

Publié le : 2019-06-20

DOI : 10.5802/jedp.667

Classification : 35P25, 45Q05, 35J10

Affiliations des auteurs :

Caro, Pedro ¹ ; Rogers, Keith M. ²

¹ BCAM - Basque Center for Applied Mathematics 48009 Bilbao Spain and Ikerbasque, Basque Foundation for Science 48011 Bilbao Spain
² Instituto de Ciencias Matemáticas CSIC-UAM-UC3M-UCM 28049 Madrid Spain

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Caro, Pedro; Rogers, Keith M. Unique determination of the electric potential in the presence of a fixed magnetic potential in the plane. Journées équations aux dérivées partielles (2018), Exposé no. 7, 9 p.. doi: 10.5802/jedp.667

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