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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Strong unique continuation for $ m$-th powers of a Laplacian operator with singular coefficients


Author: Ching-Lung Lin
Journal: Proc. Amer. Math. Soc. 135 (2007), 569-578
MSC (2000): Primary 54C40, 14E20; Secondary 46E25, 20C20
Published electronically: August 2, 2006
MathSciNet review: 2255304
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Abstract: In this paper we prove strong unique continuation for $ u$ satisfying an inequality of the form $ \vert\triangle^m u\vert \leq f(x,u,Du,\cdots,D^ku)$, where $ k$ is up to $ [3m/2]$. This result gives an improvement of a work by Colombini and Grammatico (1999) in some sense. The proof of the main theorem is based on Carleman estimates with three-parameter weights $ \vert x\vert^{2\sigma_1}(\log\vert x\vert)^{2\sigma_2}\exp (\frac{\beta}{2}(\log \vert x\vert)^2)$.


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Additional Information

Ching-Lung Lin
Affiliation: Department of Mathematics, National Chung-Cheng University, Chia-Yi 62117, Taiwan
Email: cllin@math.ccu.edu.tw

DOI: http://dx.doi.org/10.1090/S0002-9939-06-08740-5
PII: S 0002-9939(06)08740-5
Received by editor(s): August 23, 2005
Published electronically: August 2, 2006
Additional Notes: The author was supported in part by the Taiwan National Science Council, NSC 93-2119-M-194-007.
Communicated by: David S. Tartakoff
Article copyright: © Copyright 2006 American Mathematical Society