Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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On the completeness of the Papkovich-Neuber solution


Author: Ton Tran Cong
Journal: Quart. Appl. Math. 47 (1989), 645-659
MSC: Primary 73C05
DOI: https://doi.org/10.1090/qam/1031682
MathSciNet review: MR1031682
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  • [2] H. Neuber, Kerbspannungslere, Springer, Berlin, 1937
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  • [5] M. E. Gurtin, The linear theory of elasticity, Handbuch der Physik, VI a/2, Springer-Verlag, Berlin-Heidelberg-New York, 1972
  • [6] R. A. Eubanks and E. Sternberg, On the completeness of the Boussinesq-Papkovich stress functions, J. Rational Mech. Anal. 5, 735-746 (1956) MR 0079897
  • [7] M. G. Slobodyansky, General forms of solutions, expressed by harmonic functions, of the equations of elasticity for simply connected and multiply connected regions, Akad. Nauk SSSR Prikl. Mat. Mekh. 18, 54-78 (1954) MR 0064605
  • [8] I. S. Sokolnikoff, Mathematical Theory of Elasticity, 2nd ed., McGraw-Hill, New York, 1956 MR 0075755
  • [9] M. Stippes, Completeness of the Papkovich potentials, Quart. Appl. Math. 26, 477-483 (1969) MR 0239801
  • [10] S. G. Mikhlin, Multidimensional Singular Integrals and Integral Equations, Pergamon Press, New York, 1953 MR 0185399
  • [11] Ton Tran-Cong and G. P. Steven, On the representation of elastic displacement fields in terms of three harmonic functions, J. Elasticity 9, 325-333 (1979) MR 547720
  • [12] O. D. Kellog, Foundations of Potential Theory, Springer, 1929, also Dover, New York, 1953 MR 0222317

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DOI: https://doi.org/10.1090/qam/1031682
Article copyright: © Copyright 1989 American Mathematical Society

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