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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References | Similar Articles | Additional Information

**[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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Additional Information

DOI:
https://doi.org/10.1090/qam/450770

Article copyright:
© Copyright 1976
American Mathematical Society