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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. (English. Russian original) Zbl 0448.35039
Sib. Math. J. 19, 813-822 (1979); translation from Sib. Mat. Zh. 19, 1154-1165 (1978).

MSC:
35J40 Boundary value problems for higher-order elliptic equations
31B35 Connections of harmonic functions with differential equations in higher dimensions
74G50 Saint-Venant’s principle
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References:
[1] A. J. C. Barre Saint-Venant, ?De la torsion des prismes,? Mem. Divers. Savants, Acad. Sci. Paris,14, 233-560 (1855).
[2] M. E. Gurtin, ?The linear theory of elasticity,? in: Handbuch der Physik, VIa/2, Springer-Verlag, Berlin (1972).
[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). · doi:10.1007/BF00253046
[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). · Zbl 0283.73005 · doi:10.1007/BF00281492
[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).
[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.
[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). · Zbl 0077.31501 · doi:10.1002/cpa.3160100305
[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).
[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). · Zbl 0311.35008
[10] R. Toupin, ?Saint-Venant’s principle,? Arch. Rat. Mech. Anal.,18, No. 2, 83-96 (1965). · Zbl 0203.26803 · doi:10.1007/BF00282253
[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). · Zbl 0381.35068 · doi:10.1080/03605307708820051
[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).
[13] S. L. Sobolev, ?On a boundary problem for polyharmonic equations,? Mat. Sb.,2 467-500 (1937).
[14] S. L. Sobolev, Applications of Functional Analysis in Mathematical Physics, Amer. Math. soc. (1968). · Zbl 0162.35001
[15] L. Collatz, Eigenfunction Problems [Russian translation], Nauka, Moscow (1968). · Zbl 0208.40202
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