Unique continuation for the system of elasticity in the plane
HTML articles powered by AMS MathViewer
- by L. Escauriaza PDF
- Proc. Amer. Math. Soc. 134 (2006), 2015-2018 Request permission
Abstract:
We prove the strong unique continuation property for the Lamé system of elastostatics in the plane, $\nabla \cdot \left (\mu \left (\nabla u+\nabla u^t \right ) \right )+\nabla \left (\lambda \nabla \cdot u\right )=0$, with variable Lamé coefficients $\mu$, $\lambda$, when $\mu$ is Lipschitz and $\lambda$ is measurable.References
- Dang Ding Ang, Masaru Ikehata, Dang Duc Trong, and Masahiro Yamamoto, Unique continuation for a stationary isotropic Lamé system with variable coefficients, Comm. Partial Differential Equations 23 (1998), no. 1-2, 371–385. MR 1608540, DOI 10.1080/03605309808821349
- G. Alessandrini and R. Magnanini, Elliptic equations in divergence form, geometric critical points of solutions, and Stekloff eigenfunctions, SIAM J. Math. Anal. 25 (1994), no. 5, 1259–1268. MR 1289138, DOI 10.1137/S0036141093249080
- Giovanni Alessandrini and Antonino Morassi, Strong unique continuation for the Lamé system of elasticity, Comm. Partial Differential Equations 26 (2001), no. 9-10, 1787–1810. MR 1865945, DOI 10.1081/PDE-100107459
- Lipman Bers, Fritz John, and Martin Schechter, Partial differential equations, Lectures in Applied Mathematics, Vol. III, Interscience Publishers, a division of John Wiley & Sons, Inc., New York-London-Sydney, 1964. With special lectures by Lars Garding and A. N. Milgram. MR 0163043
- L. Bers and L. Nirenberg, On a representation theorem for linear elliptic systems with discontinuous coefficients and its applications, Convegno Internazionale sulle Equazioni Lineari alle Derivate Parziali, Trieste, 1954, Edizioni Cremonese, Roma, 1955, pp. 111–140. MR 0076981
- B. Dehman and L. Robbiano, La propriété du prolongement unique pour un système elliptique. Le système de Lamé, J. Math. Pures Appl. (9) 72 (1993), no. 5, 475–492 (French). MR 1239100
- K. O. Friedrichs, On the boundary-value problems of the theory of elasticity and Korn’s inequality, Ann. of Math. (2) 48 (1947), 441–471. MR 22750, DOI 10.2307/1969180
- Ching-Lung Lin, Strong unique continuation for an elasticity system with residual stress, Indiana Univ. Math. J. 53 (2004), no. 2, 557–582. MR 2060045, DOI 10.1512/iumj.2004.53.2355
- Ching-Lung Lin and Jenn-Nan Wang, Strong unique continuation for the Lamé system with Lipschitz coefficients, Math. Ann. 331 (2005), no. 3, 611–629. MR 2122542, DOI 10.1007/s00208-004-0597-z
- Gen Nakamura and Jenn-Nan Wang, Unique continuation for an elasticity system with residual stress and its applications, SIAM J. Math. Anal. 35 (2003), no. 2, 304–317. MR 2001103, DOI 10.1137/S003614100139974X
- Norbert Weck, Außenraumaufgaben in der Theorie stationärer Schwingungen inhomogener elastischer Körper, Math. Z. 111 (1969), 387–398 (German). MR 263295, DOI 10.1007/BF01110749
- Norbert Weck, Unique continuation for systems with Lamé principal part, Math. Methods Appl. Sci. 24 (2001), no. 9, 595–605. MR 1834916, DOI 10.1002/mma.231
Additional Information
- L. Escauriaza
- Affiliation: Departamento de Matematicas, Universidad del País Vasco / Euskal Herriko Unibertsitatea, Apartado 644, 48080 Bilbao, Spain
- MR Author ID: 64095
- Email: mtpeszul@lg.ehu.es
- Received by editor(s): December 7, 2004
- Received by editor(s) in revised form: February 9, 2005
- Published electronically: December 19, 2005
- Additional Notes: The author was supported by MEC grant MTM2004-03029 and by the European Commission via the network Harmonic Analysis and Related Problems, project number RTN2-2001-00315.
- Communicated by: David S. Tartakoff
- © Copyright 2005
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 134 (2006), 2015-2018
- MSC (2000): Primary 35J45; Secondary 35B60
- DOI: https://doi.org/10.1090/S0002-9939-05-08413-3
- MathSciNet review: 2215770