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Oleinik, O. A.; Yosifian, G. A.

On the asymptotic behaviour at infinity of solutions in linear elasticity. (English) Zbl 0491.73008

Arch. Ration. Mech. Anal. 78, 29-53 (1982).
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Cited in 2 Reviews
Cited in 29 Documents

MSC:

74B05 Classical linear elasticity
74G50 Saint-Venant’s principle
74B99 Elastic materials
74H99 Dynamical problems in solid mechanics
35B40 Asymptotic behavior of solutions to PDEs

Keywords:

unbounded domain; cylinder with axis parallel to 0x; vector-valued function satisfies homogeneous boundary conditions of second boundary value problem; a priori estimates; existence; converges to rigid displacement
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References:

[1] R. A. Toupin, Saint-Venant’s principle. Arch. Rational Mech. Anal., 1965, 18, no. 2, 83–96. · Zbl 0203.26803 · doi:10.1007/BF00282253
[2] J. K. Knowles, On Saint-Venant’s Principle in the two dimensional theory of elasticity. Arch. Rational Mech. Anal., 1966, 21, 1–22. · doi:10.1007/BF00253046
[3] O. A. Oleinik & G. A. Yosifian, Saint-Venant’s Principle in plane elasticity and boundary value problems for the biharmonic equation in unbounded domains. Sibirski Mat. Journ., 1978, v. 19, no. 5, 1154–1165.
[4] O. A. Oleinik & G. A. Yosifian, A mixed boundary value problem for the system of elasticity and Saint-Venant’s Principle. Collection of papers ”Complex analysis and its applications”. Moscow, Nauka, 1977. · Zbl 0381.35068
[5] G. Fichera, Remarks on Saint-Venant’s Principle. Collection of papers Complex analysis and its applications, Moscow, Nauka, 1977.
[6] N. Weck, An explicit Saint-Venant’s Principle in three-dimensional elasticity. Lect. Notes in Math. 564, 1976, 518. · Zbl 0352.73013 · doi:10.1007/BFb0087370
[7] O. A. Oleinik & G. A. Yosifian, On singularities at the boundary points and uniqueness theorems for solutions of the first boundary value problem of elasticity. Comm. in Part. Diff. Eqs., 1977, v. 2, no. 9, 937–969. · Zbl 0381.35068 · doi:10.1080/03605307708820051
[8] O. A. Oleinik, G. A. Yosifian, & I. N. Tavkhelidze, On the asymptotic behaviour of solutions of the biharmonic equation in a neighbourhood of nonregular boundary points and at infinity. Trudi Moscow Math. Society, v. 42, 1980, 160–175.
[9] I. Kopacek & O. A. Oleinik, On the asymptotic properties of solutions of the system of elasticity, Uspehi Mat. Nauk, 1978, v. 33, no. 5, 189–190.
[10] O. A. Oleinik, G. A. Yosifian, & I. N. Tavkhelidze, Estimates of solutions of the biharmonic equation near nonregular boundary points and at infinity. Uspehi Mat. Nauk, 1978, v. 33, no. 3, 181–182.
[11] A. L. Goldenweiser, Theory of thin elastic shells, 2nd edition, Nauka, Moscow, 1976. · Zbl 0060.42103
[12] M. I. Gusein-Zade, On the plane problem of elasticity in a semi-strip. Prikladnaja Mat. i Mech., v. 41, no. 1, 1977, 124–133.
[13] G. P. Panasenko, Higher order asymptotics of solutions of equations with rapidly oscillating coefficients. Dokladi AN SSSR, v. 240, no. 6, 1978, 1293–1296.
[14] O. A. Oleinik & G. A. Yosifian, On the behaviour at infinity of solutions of second order elliptic equations in domains with non-compact boundaries. Matem. Sbornik 1980, 112 (154), no. 4, 588–610.
[15] G. Fichera, Existence theorems in elasticity. Handbuch der Physik, Band VI/a2. Springer-Verlag. · Zbl 0317.73008
[16] L. Hörmander, Linear differential operators. Springer-Verlag, 1963.
[17] L. V. Kantorovich & G. P. Akilov, Functional Analysis. Moscow, Nauka, 1977.
[18] P. P. Mosolov & V. P. Miasnikov, A proof of Korn’s inequality, Dokladi AN SSSR, v. 201, no. 1, 1971, 36–39.
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