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
Full-text PDF Free Access
References |
Similar Articles |
Additional Information
Gurtin, Morton E., The linear theory of elasticity, in Encyclopedia of physics, C. Truesdell, ed., New York: Springer, 1972, Vol. 6a, Part 2
Knowles, James K., A Saint-Venant principle for a class of second-order elliptic boundary-value problems, ZAMP 18, 473–490 (1967)
- 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 272242, DOI https://doi.org/10.1007/BF01627942
- 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 366152, DOI https://doi.org/10.1007/BF01591502
- 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 324204, DOI https://doi.org/10.1512/iumj.1973.23.23020
- Walter Littman, A strong maximum principle for weakly $L$-subharmonic functions, J. Math. Mech. 8 (1959), 761–770. MR 0107746, DOI https://doi.org/10.1512/iumj.1959.8.58048
- Murray H. Protter and Hans F. Weinberger, Maximum principles in differential equations, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1967. MR 0219861
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)
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)
Horgan, Cornelius O. and Lewis T. Wheeler, Maximum principles and pointwise error estimates for torsion of shells of revolution, J. of Elasticity (to appear)
Gurtin, Morton E., The linear theory of elasticity, in Encyclopedia of physics, C. Truesdell, ed., New York: Springer, 1972, Vol. 6a, Part 2
Knowles, James K., A Saint-Venant principle for a class of second-order elliptic boundary-value problems, ZAMP 18, 473–490 (1967)
Ho, Chee-Leung and James K. Knowles, Energy inequalities and error estimates for torsion of elastic shells of revolution, ZAMP 21, 352–377 (1970)
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)
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)
Littman, Walter, A strong maximum principle for weakly L-subharmonic functions, J. Math. and Mech. 8, 761–770 (1959)
Protter, M. H. and H. F. Weinberger, Maximum principles in differential equations, Prentice-Hall, New Jersey, 1967
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)
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)
Horgan, Cornelius O. and Lewis T. Wheeler, Maximum principles and pointwise error estimates for torsion of shells of revolution, J. of Elasticity (to appear)
Similar Articles
Retrieve articles in Quarterly of Applied Mathematics
with MSC:
35J15
Retrieve articles in all journals
with MSC:
35J15
Additional Information
Article copyright:
© Copyright 1976
American Mathematical Society
