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Quantitative estimates of unique continuation for parabolic equations and inverse initial-boundary value problems with unknown boundaries


Authors: B. Canuto, E. Rosset and S. Vessella
Journal: Trans. Amer. Math. Soc. 354 (2002), 491-535
MSC (2000): Primary 35R30; Secondary 35R25, 35R35
DOI: https://doi.org/10.1090/S0002-9947-01-02860-4
Published electronically: September 26, 2001
MathSciNet review: 1862557
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Abstract: In this paper we obtain quantitative estimates of strong unique continuation for solutions to parabolic equations. We apply these results to prove stability estimates of logarithmic type for an inverse problem consisting in the determination of unknown portions of the boundary of a domain $\Omega$ in $\mathbb{R}^{n}$, from the knowledge of overdetermined boundary data for parabolic boundary value problems.


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Additional Information

B. Canuto
Affiliation: Laboratoire de Maths Appliquées, Université de Versailles-St. Quentin, Bâtiment Fermat 45, Avenue des États-Unis, 78035 Versailles Cedex, France
Email: canuto@math.uvsq.fr

E. Rosset
Affiliation: Dipartimento di Scienze Matematiche, Università degli Studi di Trieste, Via Valerio 12/1, 34100 Trieste, Italy
Email: rossedi@univ.trieste.it

S. Vessella
Affiliation: Dipartimento di Matematica per le Decisioni (DIMAD), Università degli Studi di Firenze, Via C. Lombroso 6/17, 50134 Firenze, Italy
Email: vessella@ds.unifi.it

DOI: https://doi.org/10.1090/S0002-9947-01-02860-4
Keywords: Parabolic equations, strong unique continuation, stability, inverse problems
Received by editor(s): September 25, 2000
Published electronically: September 26, 2001
Additional Notes: Work supported in part by MURST
Article copyright: © Copyright 2001 American Mathematical Society

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