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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

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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DOI: http://dx.doi.org/10.1090/S0002-9947-1990-0958886-6
PII: S 0002-9947(1990)0958886-6
Article copyright: © Copyright 1990 American Mathematical Society