Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



A two-dimensional Saint-Venant principle for second-order linear elliptic equations

Authors: Lewis T. Wheeler and Cornelius O. Horgan
Journal: Quart. Appl. Math. 34 (1976), 257-270
MSC: Primary 35J15
DOI: https://doi.org/10.1090/qam/450770
MathSciNet review: 450770
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  • [1] Gurtin, Morton E., The linear theory of elasticity, in Encyclopedia of physics, C. Truesdell, ed., New York: Springer, 1972, Vol. 6a, Part 2
  • [2] Knowles, James K., A Saint-Venant principle for a class of second-order elliptic boundary-value problems, ZAMP 18, 473-490 (1967)
  • [3] Ho, Chee-Leung and James K. Knowles, Energy inequalities and error estimates for torsion of elastic shells of revolution, ZAMP 21, 352-377 (1970) MR 0272242
  • [4] Wheeler, Lewis T., Matias J. Turteltaub and Cornelius O. Horgan, A Saint-Venant principle for the gradient in the Neumann problem, ZAMP 26, 141-154 (1975) MR 0366152
  • [5] Protter, M. H. and H. F. Weinberger, A maximum principle and gradient bounds for linear elliptic equations, Indiana U. Math. J. 23, 239-249 (1973) MR 0324204
  • [6] Littman, Walter, A strong maximum principle for weakly L-subharmonic functions, J. Math. and Mech. 8, 761-770 (1959) MR 0107746
  • [7] Protter, M. H. and H. F. Weinberger, Maximum principles in differential equations, Prentice-Hall, New Jersey, 1967 MR 0219861
  • [8] Wheeler, Lewis T. and Cornelius O. Horgan, Upper and lower bounds for the shear stress in the Saint-Venant theory of flexure, J. of Elasticity 6 (1976)
  • [9] Horgan, Cornelius O. and Lewis T. Wheeler, Saint-Venant's principle and the torsion of thin shells of revolution, J. of Applied Mechanics (Trans. ASME) 43 (1976)
  • [10] Horgan, Cornelius O. and Lewis T. Wheeler, Maximum principles and pointwise error estimates for torsion of shells of revolution, J. of Elasticity (to appear)

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DOI: https://doi.org/10.1090/qam/450770
Article copyright: © Copyright 1976 American Mathematical Society

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