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Unique continuation for $ \Delta+v$ and the C. Fefferman-Phong class

Authors: Sagun Chanillo and Eric Sawyer
Journal: Trans. Amer. Math. Soc. 318 (1990), 275-300
MSC: Primary 35J10; Secondary 35B99
MathSciNet review: 958886
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Abstract: We show that the strong unique continuation property holds for the inequality $ \left\vert {\Delta u} \right\vert \leq \left\vert \upsilon \right\vert\left\vert u \right\vert$, where the potential $ \upsilon (x)$ satisfies the C. Fefferman-Phong condition in a certain range of $ p$ values. We also deal with the situation of $ u(x)$ vanishing at infinity. These are all consequences of appropriate Carleman inequalities.

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