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ISSN 1088-6826(e) ISSN 0002-9939(p)

Remark on the strong unique continuation property for parabolic operators

Author(s): Giovanni Alessandrini; Sergio Vessella
Journal: Proc. Amer. Math. Soc. 132 (2004), 499-501.
MSC (2000): Primary 35B05, 35K99; Secondary 35R25
Posted: June 23, 2003
MathSciNet review: 2022375
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Abstract | References | Similar articles | Additional information

Abstract: We consider solutions , in a neighbourhood of , 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 , then $u( \cdot ,0) \equiv 0$ .

References:

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2.: Bers, L. Local behavior of solutions of general linear elliptic equations, Comm. Pure Appl. Math. 8 (1955), 473-496. MR 17:743a
3.: Escauriaza, L. and Fernandez, F. J., Unique continuation for parabolic operators, to appear in Ark. Mat.
4.: Fernandez, F.J., Unique continuation for parabolic operators II, preprint.
5.: Han, Qing, On the Schauder estimates of solutions to parabolic equations, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 27(1) (1998), 1-26. MR 2000a:35094
6.: Lin, Fang-Hua, A uniqueness theorem for parabolic equations. Comm. Pure Appl. Math. 43(1) (1990), 127-136. MR 90j:35106

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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: 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
Posted: June 23, 2003
Additional Notes: The authors acknowledge partial support from M.U.R.S.T. grant no. MM01111258.
Communicated by: Andreas Seeger
Copyright of article: Copyright 2003, American Mathematical Society

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