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

 

On a question of Landis and Oleinik


Author: Tu A. Nguyen
Journal: Trans. Amer. Math. Soc. 362 (2010), 2875-2899
MSC (2000): Primary 35K99
Published electronically: January 4, 2010
MathSciNet review: 2592940
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Abstract: Let $ P=\partial_{t}+\partial_{i}(a^{ij}\partial_{j})$ be a backward parabolic operator. It is shown that under certain conditions on $ \left\{ a^{ij}\right\} $, if $ u$ satisfies $ \left\vert Pu\right\vert\leq$ $ C(\left\vert u\right\vert+\left\vert\nabla u\right\vert)$, $ \left\vert u(x,t)\right\vert\lesssim e^{C\left\vert x\right\vert^{2}}$ in $ \mathbb{R}^{n}\times[0,T]$ and $ \left\vert u(x,0)\right\vert\lesssim e^{-M\left\vert x\right\vert^{2}}$ for all $ M>0$, then $ u$ vanishes identically in $ \mathbb{R}^{n}\times[0,T]$.


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Additional Information

Tu A. Nguyen
Affiliation: Department of Mathematics, University of Chicago, 5734 S. University Ave., Chicago, Illinois 60637
Address at time of publication: Department of Mathematics, University of Washington, Box 354350, Seattle, Washington 98195-4350
Email: tu@math.uchicago.edu, anhtu@math.washington.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-10-04733-1
PII: S 0002-9947(10)04733-1
Received by editor(s): October 29, 2007
Published electronically: January 4, 2010
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.