Pacific Journal of Mathematics

Physical interpretation and strengthing of M. Protter's method for vibrating nonhomogeneous membranes; its analogue for Schrödinger's equation.

Joseph Hersch

Article information

Source
Pacific J. Math., Volume 11, Number 3 (1961), 971-980.

Dates
First available in Project Euclid: 14 December 2004

Permanent link to this document
https://projecteuclid.org/euclid.pjm/1103037130

Mathematical Reviews number (MathSciNet)
MR0151715

Zentralblatt MATH identifier
0109.43301

Subjects
Primary: 35.75
Secondary: 35.77

Citation

Hersch, Joseph. Physical interpretation and strengthing of M. Protter's method for vibrating nonhomogeneous membranes; its analogue for Schrödinger's equation. Pacific J. Math. 11 (1961), no. 3, 971--980. https://projecteuclid.org/euclid.pjm/1103037130


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References

  • [1] R. Courant and D. Hubert, Methoden der mathematschenPhysik,vol. I, Springer, Berlin (1931).
  • [2] J. Hersch, Une interpretationdu principe de Thomson et son analogue pour la frequence fondamentale d'une membrane. Application. C. R. Acad. Sci. Paris, 248 (1959), 2060.
  • [3] Un principe de maximum pour la frequence fondamentale d'une membrane, C. R. Acad. Sci. Paris, 249 (1959), 1074.
  • [4] Sur quelques prncipes extremaux de la physique mathematique, Lnseignement Math., 2e serie, 5 (1959), 249-257.
  • [5] Sur la frequence fondamentaled'une membrane vibrante: evaluations par defaut et principe de maximum, ZAMP, 11 (1960), 387-413.
  • [6] L. E. Payne and H. F. Weinberger, Lower bounds for vibration frequencies of elastically supported membranes and plates, J. Soc. Indust. Appl. Math., 5 (1957), 171-182.
  • [7] M. H. Protter, Lower bounds for the first eigenvalue of elliptic equations and related topics, Tech. Report No. 8, AFOSR, University of California, Berkeley (1958).
  • [8] Vibration of a nonhomogeneous membrane, Pacific J. Math., 9 (1959), 1249-1255. INSTITUT BATTELLE, GENEVA SWITZERLAND