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arXiv · 1901.04814

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

Pedro Caro·Keith M. Rogers
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Abstract

For potentials $V\in L^\infty(\mathbb{R}^2,\mathbb{R})$ and $A\in W^{1,\infty}(\mathbb{R}^2,\mathbb{R}^2)$ with compact support, we consider the Schr\"odinger equation $-(\nabla +iA)^2 u+Vu=k^2u$ 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 Schr\"odinger equation.

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Pedro Caro, Keith M. Rogers. 2019-01-15. Unique determination of the electric potential in the presence of a fixed magnetic potential in the plane. https://arxiv.org/abs/1901.04814

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