Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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

   
 
 

 

An extension of the method of Trefftz for finding local bounds on the solutions of boundary value problems, and on their derivatives


Author: Philip Cooperman
Journal: Quart. Appl. Math. 10 (1953), 359-373
MSC: Primary 36.0X
DOI: https://doi.org/10.1090/qam/52010
MathSciNet review: 52010
Full-text PDF Free Access

References | Similar Articles | Additional Information

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

  • [E] Trefftz, Ein Gegenstück zum Ritzschen Verfahren, Proc. 2nd Int. Congress Appl. Mech., Zurich, 131, (1926). Konvergenz und Fehlerschätzung beim Ritzschen Verfahren, Math. Ann. 100, 503, (1928). MR 1512498
  • [K] O. Friedrichs, Die Randwert-und-Eigenwertprobleme aus der Theorie der elastischen Platten, Math. Ann. 98, 206, (1927-28). Ein Verfahren der Variationsrechnung..., Nach. der Ges. d. Wiss. zu Gottingen, 13, 1929.
  • [R] Courant and D. Hilbert, Die Methoden der Mathematischen Physik, 1, Interscience Publishers, New York, 1943, 228-231; 199-209; 2, Chap. 7. MR 0009069
  • [J] L. Synge, The method of the hypercircle in function-space for boundary-value problems, Proc. Roy. Soc. A 191, 447, (1947). MR 0025903
  • 1. Upper and lower bounds for the solutions of problems in elasticity, Proc. Roy. Irish Acad. 53A, 41, (1950). MR 0039484
  • 2. Pointwise bounds for the solutions of certain boundary-value problems, Proc. Roy. Soc. A 208, 170, (1951). MR 0043281
  • [W] Prager and J. L. Synge, Approximations in elasticity based on the concept of function space, Q. Appl. Math, 5, 241, (1947). MR 0025902
  • [H] J. Greenberg, The determination of upper and lower bounds for the solution of the Dirichlet problem, J. Math. Phys. 27, 161, (1948). MR 0026171
  • [J] B. Diaz and H. J. Greenberg, Upper and lower bounds for the solutions of the first biharmonic boundary value problem, J. Math Phys. 27, 193, (1948). MR 0026862
  • [J] B. Diaz and A. Weinstein, Schwarz's inequality and the methods of Rayleigh-Ritz and Trefftz, J. Math. Phys. 27, 133, (1948). MR 0022458
  • [J] B. Diaz, Upper and lower bounds for quadratic functionals, Proc. Symposium on Spectral Theory, Oklahoma A. & M. College, Stillwater, 279, 1951. MR 0043280
  • [P] Cooperman, The Legendre Transformation, Master's thesis (unpub.) New York University (1948).
  • [C] G. Maple, The Dirichlet problem: bounds at a point for the solution and its derivatives, QAM, 213, (1950). MR 0040499
  • [A] J. McConnell, The hypercircle of approximation for a system of partial differential equations of the second order, Proc. Roy. Irish Acad., 41, 53A.

Similar Articles

Retrieve articles in Quarterly of Applied Mathematics with MSC: 36.0X

Retrieve articles in all journals with MSC: 36.0X


Additional Information

DOI: https://doi.org/10.1090/qam/52010
Article copyright: © Copyright 1953 American Mathematical Society

American Mathematical Society