Remark on the strong unique continuation property for parabolic operators
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- by Giovanni Alessandrini and Sergio Vessella PDF
- Proc. Amer. Math. Soc. 132 (2004), 499-501 Request permission
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 $u( \cdot ,0) \equiv 0$.References
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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
- 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
- © Copyright 2003 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 132 (2004), 499-501
- MSC (2000): Primary 35B05, 35K99; Secondary 35R25
- DOI: https://doi.org/10.1090/S0002-9939-03-07142-9
- MathSciNet review: 2022375