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

Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 in , 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