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

 

Remark on the strong unique continuation property for parabolic operators


Authors: Giovanni Alessandrini and Sergio Vessella
Journal: Proc. Amer. Math. Soc. 132 (2004), 499-501
MSC (2000): Primary 35B05, 35K99; Secondary 35R25
Published electronically: June 23, 2003
MathSciNet review: 2022375
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Abstract: We consider solutions $u = u(x,t)$, in a neighbourhood of $(x,t) =(0,0)$, to a parabolic differential equation with variable coefficients depending on space and time variables. We assume that the coefficients in the principal part are Lipschitz continuous and that those in the lower order terms are bounded. We prove that, if $u( \cdot,0)$ vanishes of infinite order at $x=0$, then $u( \cdot ,0) \equiv 0$.


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Additional Information

Giovanni Alessandrini
Affiliation: Dipartimento di Scienze Matematiche, Universitá degli Studi di Trieste, Via A. Valerio 12/1, 34127 Trieste, Italy
Email: alessang@univ.trieste.it

Sergio Vessella
Affiliation: DiMaD, Universitá degli Studi di Firenze, Via C. Lombroso 6/17, 50134 Florence, Italy
Email: vessella@dmd.unifi.it

DOI: http://dx.doi.org/10.1090/S0002-9939-03-07142-9
PII: S 0002-9939(03)07142-9
Keywords: Strong unique continuation, parabolic equations
Received by editor(s): October 15, 2002
Published electronically: June 23, 2003
Additional Notes: The authors acknowledge partial support from M.U.R.S.T. grant no. MM01111258.
Communicated by: Andreas Seeger
Article copyright: © Copyright 2003 American Mathematical Society