Energy estimates for the biharmonic equation in three dimensions
Author:
Chang Hao Lin
Journal:
Quart. Appl. Math. 52 (1994), 649-663
MSC:
Primary 73C10; Secondary 35Q99
DOI:
https://doi.org/10.1090/qam/1306042
MathSciNet review:
MR1306042
Full-text PDF Free Access
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Additional Information
J. K. Knowles, An energy estimate for the biharmonic equation and its application to Saint-Venant’s principle in plane elastostatistics, Indian J. Pure Appl. Math. 14, 791–805 (1983)
J. K. Knowles, On Saint-Venant’s principle in the two dimensional linear theory of elasticity, Arch. Rational Mech. Anal. 21, 1–22 (1966)
C. O. Horgan, Decay estimates for the biharmonic equation with applications to Saint-Venant’s principles in plane elasticity and Stokes flows, Quart. Appl. Math. 47, 147–157 (1989)
C. O. Horgan and J. K. Knowles, Recent developments concerning Saint-Venant’s principle, T. Y. Wu and J. W. Hutchinson (eds.), Adv. Appl. Mech. 23, Academic Press, San Diego, 1983, pp. 179–269
J. N. Flavin, On Knowles’ version of Saint-Venant’s principle in two dimensional elastostatics, Arch. Rational Mech. Anal. 53, 366–375 (1974)
O. A. Oleinik and G. A. Yosifian, The Saint-Venant’s principle in the two-dimensional theory of elasticity and boundary problems for a biharmonic equation in unbounded domains, Sibirsk. Math. Zh. 19, 1154–1165 (1978); English transl., Siberian Math. J. 19, 813–822 (1978)
K. A. Ames and L. E. Payne, Decay estimates in steady pipe flow, SIAM J. Math. Anal. 20, 789–815 (1989)
G. Faber, Beweis, dass under allen homogenen membranen von gleicher Fläche und gleicher Spannung die kreisförmige den tiefsten Grundton gibt, Sitz Bayer Akad. Wiss., 169–192 (1923)
G. Pólya and G. Szegö, Isoperimetric inequalities in mathematical physics, Ann. of Math. Stud. 27, Princeton Univ. Press, Princeton, NJ, 1951
C. O. Horgan, Recent developments concerning Saint-Venant’s principle: an update, Appl. Mech. Rev. 42, 295–303 (1989)
J. K. Knowles, An energy estimate for the biharmonic equation and its application to Saint-Venant’s principle in plane elastostatistics, Indian J. Pure Appl. Math. 14, 791–805 (1983)
J. K. Knowles, On Saint-Venant’s principle in the two dimensional linear theory of elasticity, Arch. Rational Mech. Anal. 21, 1–22 (1966)
C. O. Horgan, Decay estimates for the biharmonic equation with applications to Saint-Venant’s principles in plane elasticity and Stokes flows, Quart. Appl. Math. 47, 147–157 (1989)
C. O. Horgan and J. K. Knowles, Recent developments concerning Saint-Venant’s principle, T. Y. Wu and J. W. Hutchinson (eds.), Adv. Appl. Mech. 23, Academic Press, San Diego, 1983, pp. 179–269
J. N. Flavin, On Knowles’ version of Saint-Venant’s principle in two dimensional elastostatics, Arch. Rational Mech. Anal. 53, 366–375 (1974)
O. A. Oleinik and G. A. Yosifian, The Saint-Venant’s principle in the two-dimensional theory of elasticity and boundary problems for a biharmonic equation in unbounded domains, Sibirsk. Math. Zh. 19, 1154–1165 (1978); English transl., Siberian Math. J. 19, 813–822 (1978)
K. A. Ames and L. E. Payne, Decay estimates in steady pipe flow, SIAM J. Math. Anal. 20, 789–815 (1989)
G. Faber, Beweis, dass under allen homogenen membranen von gleicher Fläche und gleicher Spannung die kreisförmige den tiefsten Grundton gibt, Sitz Bayer Akad. Wiss., 169–192 (1923)
G. Pólya and G. Szegö, Isoperimetric inequalities in mathematical physics, Ann. of Math. Stud. 27, Princeton Univ. Press, Princeton, NJ, 1951
C. O. Horgan, Recent developments concerning Saint-Venant’s principle: an update, Appl. Mech. Rev. 42, 295–303 (1989)
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Article copyright:
© Copyright 1994
American Mathematical Society
