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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Unique continuation for $\Delta +v$ and the C. Fefferman-Phong class
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by Sagun Chanillo and Eric Sawyer PDF
Trans. Amer. Math. Soc. 318 (1990), 275-300 Request permission

Abstract:

We show that the strong unique continuation property holds for the inequality $\left | {\Delta u} \right | \leq \left | \upsilon \right |\left | u \right |$, 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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Additional Information
  • © Copyright 1990 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 318 (1990), 275-300
  • MSC: Primary 35J10; Secondary 35B99
  • DOI: https://doi.org/10.1090/S0002-9947-1990-0958886-6
  • MathSciNet review: 958886