On a question of Landis and Oleinik
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- by Tu A. Nguyen PDF
- Trans. Amer. Math. Soc. 362 (2010), 2875-2899 Request permission
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 $\left |Pu\right |\leq$ $C(\left |u\right |+\left |\nabla u\right |)$, $\left |u(x,t)\right |\lesssim e^{C\left |x\right |^{2}}$ in $\mathbb {R}^{n}\times [0,T]$ and $\left |u(x,0)\right |\lesssim e^{-M\left |x\right |^{2}}$ for all $M>0$, then $u$ vanishes identically in $\mathbb {R}^{n}\times [0,T]$.References
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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
- Received by editor(s): October 29, 2007
- Published electronically: January 4, 2010
- © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 362 (2010), 2875-2899
- MSC (2000): Primary 35K99
- DOI: https://doi.org/10.1090/S0002-9947-10-04733-1
- MathSciNet review: 2592940