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Strong uniqueness for the plate equations


Author: Shigeo Tarama
Journal: Proc. Amer. Math. Soc. 132 (2004), 3629-3639
MSC (2000): Primary 35A07, 35Q72
DOI: https://doi.org/10.1090/S0002-9939-04-07624-5
Published electronically: July 20, 2004
MathSciNet review: 2084086
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Abstract: In this paper we show the strong uniqueness for the plate equations. By using the idea due to Lebeau we transform the given operator to the elliptic operators to which we apply the Carleman estimates given by Alinhac and Lerner.


References [Enhancements On Off] (What's this?)

  • 1. S. Alinhac and N. Lerner, Unicité forte à partir d’une variété de dimension quelconque pour des inégalités différentielles elliptiques, Séminaire Goulaouic-Schwartz, 1979–1980 (French), École Polytech., Palaiseau, 1980, pp. Exp. No. 20, 10 (French). MR 600705
    S. Alinhac and N. Lerner, Unicité forte à partir d’une variété de dimension quelconque pour des inégalités différentielles elliptiques, Duke Math. J. 48 (1981), no. 1, 49–68 (French). MR 610175
  • 2. F. Colombini and C. Grammatico, Strong uniqueness for Laplace and bi-Laplace operators in the limit case, Carleman estimates and applications to uniqueness and control theory (Cortona, 1999) Progr. Nonlinear Differential Equations Appl., vol. 46, Birkhäuser Boston, Boston, MA, 2001, pp. 49–60. MR 1839166
  • 3. Victor Isakov, On uniqueness in a lateral Cauchy problem with multiple characteristics, J. Differential Equations 134 (1997), no. 1, 134–147. MR 1429094, https://doi.org/10.1006/jdeq.1996.3227
  • 4. Gilles Lebeau, Un probléme d’unicité forte pour l’équation des ondes, Comm. Partial Differential Equations 24 (1999), no. 3-4, 777–783 (French). MR 1683060, https://doi.org/10.1080/03605309908821444
  • 5. Luc Robbiano, Théorème d’unicité adapté au contrôle des solutions des problèmes hyperboliques, Comm. Partial Differential Equations 16 (1991), no. 4-5, 789–800 (French). MR 1113107, https://doi.org/10.1080/03605309108820778
  • 6. Daniel Tataru, Unique continuation for solutions to PDE’s; between Hörmander’s theorem and Holmgren’s theorem, Comm. Partial Differential Equations 20 (1995), no. 5-6, 855–884. MR 1326909, https://doi.org/10.1080/03605309508821117
  • 7. D. Tataru, Carleman estimates, unique continuation and applications, (http://www.math. berkeley.edu/~tataru/papers/)

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Additional Information

Shigeo Tarama
Affiliation: Laboratory of Applied Mathematics, Graduate School of Engineering, Osaka City University, Osaka, 558-8585, Japan
Email: starama@mech.eng.osaka-cu.ac.jp

DOI: https://doi.org/10.1090/S0002-9939-04-07624-5
Keywords: Strong uniqueness, plate equations
Received by editor(s): August 21, 2003
Published electronically: July 20, 2004
Communicated by: David S. Tartakoff
Article copyright: © Copyright 2004 American Mathematical Society