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Unique continuation for second-order parabolic operators at the initial time


Authors: Paolo Albano and Daniel Tataru
Journal: Proc. Amer. Math. Soc. 132 (2004), 1077-1085
MSC (2000): Primary 35K10, 35B60
DOI: https://doi.org/10.1090/S0002-9939-03-07227-7
Published electronically: September 18, 2003
MathSciNet review: 2045423
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Abstract | References | Similar Articles | Additional Information

Abstract: We consider second-order parabolic equations with time independent coefficients. Under reasonable assumptions, it is known that the fundamental solution satisfies certain Gaussian bounds related to the associated geodesic distance. In this article we prove a sharp unique continuation property at the initial time which matches exactly the above-mentioned kernel bounds.


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  • 1. V. Isakov, Carleman type estimates in an anisotropic case and applications, Journal of Differential Equations 105 (1993), no. 2, 217-238. MR 94k:35070
  • 2. F. H. Lin, A uniqueness theorem for parabolic equations, Comm. Pure Appl. Math. 43 (1990), 125-136. MR 90j:35106
  • 3. C.-C. Poon, Unique continuation for parabolic equations, Comm. Partial Differential Equations 21 (1996), 521-539. MR 97f:35081
  • 4. D. W. Stroock, Diffusion semigroups corresponding to uniformly elliptic divergence form operators. Séminaire de Probabilités, XXII, 316-347, Lecture Notes in Math., 1321, Springer-Verlag, Berlin, 1988. MR 90b:35071
  • 5. D. Tataru, Unique continuation for solutions to Partial Differential Equations: between Hormander's theorem and Holmgren's theorem, Comm. Partial Differential Equations 20 (1995), 855-884. MR 96e:35019
  • 6. D. Tataru, Carleman estimates, unique continuation and controllability for anisotropic PDEs, Contemporary Mathematics, Volume 209 (1997), 267-279. MR 98i:93010
  • 7. D. Tataru, Unique continuation for operators with partially analytic coefficients, J. Math. Pures Appl. 78 (1999), 505-521. MR 2000e:35005

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Additional Information

Paolo Albano
Affiliation: Dipartimento di Matematica, Università di Bologna, 40127 Bologna, Italy
Email: albano@dm.unibo.it

Daniel Tataru
Affiliation: Department of Mathematics, University of California Berkeley, Berkeley, California 94720
Email: tataru@math.berkeley.edu

DOI: https://doi.org/10.1090/S0002-9939-03-07227-7
Received by editor(s): November 19, 2002
Published electronically: September 18, 2003
Additional Notes: The second author was supported in part by NSF grant DMS 9970297
Communicated by: David S. Tartakoff
Article copyright: © Copyright 2003 American Mathematical Society

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