Strong uniqueness for the plate equations
HTML articles powered by AMS MathViewer
- by Shigeo Tarama PDF
- Proc. Amer. Math. Soc. 132 (2004), 3629-3639 Request permission
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
- 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
- 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
- Victor Isakov, On uniqueness in a lateral Cauchy problem with multiple characteristics, J. Differential Equations 134 (1997), no. 1, 134–147. MR 1429094, DOI 10.1006/jdeq.1996.3227
- 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, DOI 10.1080/03605309908821444
- 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, DOI 10.1080/03605309108820778
- 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, DOI 10.1080/03605309508821117
- D. Tataru, Carleman estimates, unique continuation and applications, (http://www.math. berkeley.edu/˜tataru/papers/)
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
- Received by editor(s): August 21, 2003
- Published electronically: July 20, 2004
- Communicated by: David S. Tartakoff
- © Copyright 2004 American Mathematical Society
- 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
- MathSciNet review: 2084086