Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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



Asymptotic behavior of periodic, periodic biharmonic and periodic harmonic functions

Author: Kenneth B. Howell
Journal: Quart. Appl. Math. 45 (1987), 279-286
MSC: Primary 31B30
DOI: https://doi.org/10.1090/qam/895097
MathSciNet review: 895097
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The behavior of periodic functions defined on domains containing the upper half space, $ \left\{ {\left( {{x^1},{x^2},...,{x^n}} \right):{x^n} > 0} \right\}$, is investigated as $ {x^n}$ approaches infinity. Bounds on some of the first order derivatives of these functions are obtained which are directly proportional to bounds on derivatives of arbitrary orders in certain directions. It is shown that a periodic biharmonic and a periodic harmonic function can be approximated, respectively, by a third degree and a first degree polynomial in the variable $ {x^n}$ and that, as $ {x^n}$ approaches infinity, the error in using this approximation vanishes faster than the reciprocal of $ {x^n}$ raised to any power.

References [Enhancements On Off] (What's this?)

  • [1] M. E. Gurtin and E. Sternberg, Theorems in linear elastostatics for exterior domains, Arch. Rat. Mech. Anal. 8, 99-119 (1961) MR 0133972
  • [2] K. B. Howell, Directionally dependent asymptotic behavior of biharmonic functions with applications to elasticity, SIAM J. Math. Anal. 16, 822-847 (1985) MR 793925
  • [3] K. B. Howell, Asymptotic behavior of periodic strain states, SIAM J. Math. Anal. 17, 197-217 (1986) MR 819223
  • [4] K. B. Howell, The asymptotic behavior of doubly periodic strain states, J. Elasticity 16, 43-61 (1986) MR 835365
  • [5] N. K. Muskhelishvili, Some basic problems of the mathematical theory of elasticity (translation by J. R. M. Radok), Noordhoff, Groningen (1953) MR 0058417

Similar Articles

Retrieve articles in Quarterly of Applied Mathematics with MSC: 31B30

Retrieve articles in all journals with MSC: 31B30

Additional Information

DOI: https://doi.org/10.1090/qam/895097
Article copyright: © Copyright 1987 American Mathematical Society

American Mathematical Society