Skip to main content
SpringerLink
Log in

On the contact problem of classical elasticity

  • Published:
Journal of Elasticity Aims and scope Submit manuscript

Abstract

We deal with the contact problem of homogeneous and isotropic linear elastostatics in the exterior of a bounded convex domain of \({\Bbb{R}}^{3}\) . We prove existence and uniqueness of a solution, provided the elasticity tensor is only strongly elliptic.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Dautray, R., Lions, J.L.: Mathematical Analysis and Numerical Methods for Science and Technology, vol. IV. Springer, Berlin (1990)

    Google Scholar 

  2. Edelstein, W.S., Fosdick, R.I.: A note on non-uniqueness in linear elasticity theory. J. Appl. Math. Phys. (ZAMP) 19, 906–912 (1968)

    Article  MATH  MathSciNet  Google Scholar 

  3. Fosdick, R.I.: On the displacement boundary-value problem of static linear elasticity theory. J. Appl. Math. Phys. (ZAMP) 19, 219–233 (1968)

    Article  MATH  MathSciNet  Google Scholar 

  4. Fosdick, R.I., Piccioni, M.D., Puglisi, G.: A note on uniqueness in linear elastostatics. J. Elast. 88, 79–86 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  5. Giusti, E.: Direct Methods in the Calculus of Variations. World Scientific, Singapore (2003)

    MATH  Google Scholar 

  6. Gurtin, M.E.: The linear theory of elasticity. In: Truesedell, C. (ed.) Handbuch der Physik, vol. VIa/2. Springer, Berlin (1972)

    Google Scholar 

  7. Kondrat’ev, V.A., Oleinik, O.A.: Boundary–value problems for the system of elasticity theory in unbounded domains. Korn’s inequalities. Usp. Mat. Nauk 43(5), 55–98 (1988) (Russian). English translation in Russ. Math. Surv. 43(5), 65–119 (1988)

    MATH  MathSciNet  Google Scholar 

  8. Kupradze, V.D., Gegelia, T.G., Basheleishvili, M.O., Burchuladze, T.V.: Three Dimensional Problems of the Mathematical Theory of Elasticity and Thermoelasticity. North-Holland, Amsterdam (1979)

    MATH  Google Scholar 

  9. Russo, R.: On Stokes’ problem. In: Rannacher, R., Sequeira, A. (eds.) Advances in Mathematical Fluid Mechanics. Springer, Berlin (2010). DOI:10.1007/978-3-642-04068-9_28

  10. Solonnikov, V.A., Ščadilov, V.E.: On a boundary value problem for a stationary system of Navier–Stokes equations. Tr. Math. Inst. Steklov 125, 196–210 (1973). English transl.: Proc. Steklov Math. Inst. 125, 186–199 (1973)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dipartimento di Matematica, Seconda Università degli Studi di Napoli, Via Vivaldi, 43, 81100, Caserta, Italy

    Antonio Russo & Alfonsina Tartaglione

Authors
  1. Antonio Russo
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Alfonsina Tartaglione
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Antonio Russo.

Additional information

"This work was supported by the research group GNFM of INDAM.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Russo, A., Tartaglione, A. On the contact problem of classical elasticity. J Elast 99, 19–38 (2010). https://doi.org/10.1007/s10659-009-9227-z

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10659-009-9227-z

Mathematics Subject Classification (2000)

Search

Navigation