zbMATH — the first resource for mathematics

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).

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
Full Text: DOI EuDML
[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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.