Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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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] Chee-leung Ho and James K. Knowles, Energy inequalities and error estimates for torsion of elastic shells of revolution, Z. Angew. Math. Phys. 21 (1970), 352–377 (English, with German summary). MR 0272242, https://doi.org/10.1007/BF01627942
  • [4] Lewis T. Wheeler, Matías J. Turteltaub, and Cornelius O. Horgan, A Saint-Venant principle for the gradient in the Neumann problem, Z. Angew. Math. Phys. 26 (1975), 141–153 (English, with German summary). MR 0366152, https://doi.org/10.1007/BF01591502
  • [5] M. H. Protter and H. F. Weinberger, A maximum principle and gradient bounds for linear elliptic equations, Indiana Univ. Math. J. 23 (1973/74), 239–249. MR 0324204, https://doi.org/10.1512/iumj.1973.23.23020
  • [6] Walter Littman, A strong maximum principle for weakly 𝐿-subharmonic functions, J. Math. Mech. 8 (1959), 761–770. MR 0107746
  • [7] Murray H. Protter and Hans F. Weinberger, Maximum principles in differential equations, Prentice-Hall, Inc., Englewood Cliffs, N.J., 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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