Abstract
A sharp uniqueness class is determined for the traction problem of linear elastostatics in exterior domains and in the half space. In particular, it is shown that this problem has a most one solution in the class of all vector fields u such that either u=o(r) or % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGafy4bIeTbaK% aaaaa!3782!\[\hat \nabla \]u=o(1), as r→+∞, with w and % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGafy4bIeTbaK% aaaaa!3782!\[\hat \nabla \]u respectively rigid displacement and symmetric part of ∇u.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
S. Campanato, Equazioni ellittiche del secondo ordine e spazi ℒ2,λ, Ann. Mat. Pura Appl. 69 (1965) 321–382.
S. Campanato, Sistemi ellittici in forma di divergenza. Regolarità all'interno, Quaderni Scuola Norm. Pisa, Pisa (1980).
B. Carbonaro and R. Russo, Sharp uniqueness classes in linear elastodynamics, J. Elasticity 27 (1992) 37–44.
G. Duvaut and J.L. Lions, Sur les inéquations en mécanique et en physique, Dunod, Paris (1972).
G. Fichera, Sull'esistenza e sul calcolo delle soluzioni dei problemi al contorno relativi all'equilibrio di un corpo elastico, Ann. Scuola Norm. Pisa (3) 4 (1950) 35–99.
G. Fichera, Existence theorems in elasticity, in Handbuch der Physik (ed. C. Truesdell), vol. VIa/2, Springer (1971) pp. 347–424.
G.P. Galdi and S. Rionero, The weight function approach to uniqueness of viscous flows in unbounded domains, Arch. Rational Mech. Anal. 69 (1979) 37–52.
M. Giaquinta, Multiple integrals in the calculus of variations and nonlinear elliptic systems, Ann. Math. Studies vol. 105, Princeton (1986).
E. Giusti, Equazioni ellittiche del secondo ordine, Quaderni dell'U.M.I., Pitagora, Bologna (1978).
M.E. Gurtin, The linear theory of elasticity, in Handbuch der Physik (ed. C. Truesdell), vol. IVa/2, Springer (1971) pp. 1–295.
M.E. Gurtin and E. Sternberg, Theorems in linear elastostatics for exterior domains, Arch. Rational Mech. Anal. 8 (1961) 99–119.
R.J. Knops and L.E. Payne, Uniqueness theorems in linear elasticity, Springer Tracts in Natural Philosophy vol. 19, Springer (1971).
V.A. Kondratiev and O.A. Oleinik, Asymptotic properties of solutions of the elasticity system, in Application of Multiple Scaling in Mechanics (ed. P.G. Ciarlet and E. Sanchez-Palencia), Masson, Paris (1987) pp. 187–205.
L.E. Payne and H. Weinberger, A note on a Lemma of Finn and Gilbarg, Acta Math. 98 (1957) 297–299.
R. Russo, Uniqueness in plane linear elastostatics for exterior domains, Bollettino UMI B (1991).
R. Russo, An extension of the basic theorems on linear elastostatics for exterior domains, Ann. Univ. Ferrara (VII) Sc. Mat. 34 (1988) 101–119.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Russo, R. On the traction problem in linear elastostatics. J Elasticity 27, 57–68 (1992). https://doi.org/10.1007/BF00057860
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00057860