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The Saint-Venant principle in the two-dimensional theory of elasticity and boundary problems for a biharmonic equation in unbounded domains

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Literature Cited

  1. A. J. C. Barre Saint-Venant, “De la torsion des prismes,” Mem. Divers. Savants, Acad. Sci. Paris,14, 233–560 (1855).

    Google Scholar 

  2. M. E. Gurtin, “The linear theory of elasticity,” in: Handbuch der Physik, VIa/2, Springer-Verlag, Berlin (1972).

    Google Scholar 

  3. J. K. Knowles, “On Saint-Venant's principle in the two-dimensional linear theory of elasticity,” Arch. Rat. Mech. Anal.,21, No. 1, 1–22 (1966).

    Google Scholar 

  4. J. N. Flavin, “On Knowles' version of Saint-Venant's principle in two-dimensional elastostatics,” Arch. Rat. Mech. Anal.,53, No. 4, 366–375 (1974).

    Google Scholar 

  5. O. A. Oleinik and G. A. Iosif'yan, “On Saint-Venant's principle in two-dimensional elasticity theory,” Dokl. Akad. Nauk SSSR,239, No. 3, 530–533 (1978).

    Google Scholar 

  6. I. I. Vorovich, “Formulation of boundary problems in elasticity theory for an infinite energy interval, and basis properties of the homogeneous solutions,” in: Mechanics of Deformed Bodies and Constructions [in Russian], Mashinostroenie, Moscow (1975), pp. 112–128.

    Google Scholar 

  7. P. D. Lax, “The Phragmen-Lindelöf theorem in harmonic analysis and its application in the theory of elliptic equations,” Commun. Pure Appl. Math.,10, No. 3, 361–389 (1957).

    Google Scholar 

  8. O. A. Oleinik and E. V. Radkevich, “Analyticity and theorems of Liouville and Phragmen-Lindelöf type for general elliptic systems of differential equations,” Mat. Sb.,95, No. 1, 130–145 (1974).

    Google Scholar 

  9. E. M. Landis, “Behavior of solutions of elliptic equations of high order in unbounded domains,” Tr. Mosk. Mat. Ob-va,31, 35–58 (1974).

    Google Scholar 

  10. R. Toupin, “Saint-Venant's principle,” Arch. Rat. Mech. Anal.,18, No. 2, 83–96 (1965).

    Google Scholar 

  11. O. A. Oleinik and G. A. Yosifian, “On singularities at the boundary points and uniqueness theorems for solutions of the first boundary problem of elasticity,” Commun. Partial Diff. Equations,2, No. 9, 937–969 (1977).

    Google Scholar 

  12. O. A. Oleinik and G. A. Iosif'yan, “The Saint-Venant principle for a mixed problem in elasticity theory and its applications,” Dokl. Akad. Nauk SSSR,233, No. 5, 824–827 (1977).

    Google Scholar 

  13. S. L. Sobolev, “On a boundary problem for polyharmonic equations,” Mat. Sb.,2 467–500 (1937).

    Google Scholar 

  14. S. L. Sobolev, Applications of Functional Analysis in Mathematical Physics, Amer. Math. soc. (1968).

  15. L. Collatz, Eigenfunction Problems [Russian translation], Nauka, Moscow (1968).

    Google Scholar 

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Translated from Sibirskii Matematicheskii Zhurnal, Vol. 19, No. 5, pp. 1154–1165, September–October, 1978.

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Oleinik, O.A., Iosif'yan, G.A. The Saint-Venant principle in the two-dimensional theory of elasticity and boundary problems for a biharmonic equation in unbounded domains. Sib Math J 19, 813–822 (1978). https://doi.org/10.1007/BF00973610

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  • DOI: https://doi.org/10.1007/BF00973610

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