Proceedings of the Japan Academy

On Schwarz's lemma for $\Delta u + c\left( x \right)u = 0$

Kyûya Masuda

Full-text: Open access

Article information

Source
Proc. Japan Acad., Volume 50, Number 8 (1974), 555-560.

Dates
First available in Project Euclid: 20 November 2007

Permanent link to this document
https://projecteuclid.org/euclid.pja/1195518833

Digital Object Identifier
doi:10.3792/pja/1195518833

Mathematical Reviews number (MathSciNet)
MR0374656

Zentralblatt MATH identifier
0306.35010

Subjects
Primary: 35J05: Laplacian operator, reduced wave equation (Helmholtz equation), Poisson equation [See also 31Axx, 31Bxx]

Citation

Masuda, Kyûya. On Schwarz's lemma for $\Delta u + c\left( x \right)u = 0$. Proc. Japan Acad. 50 (1974), no. 8, 555--560. doi:10.3792/pja/1195518833. https://projecteuclid.org/euclid.pja/1195518833


Export citation

References

  • [1] Agmon, S.: Unicite et convexite dans les problems differentielles. Sem. d'Analyse Sup., Univ. de Montreal (1965).
  • [2] Gilbarg, D., and J. Serrin: On isolated singularities of solutions of second order elliptic differential equations. J. d'Analyse Math., 4, 309-336 (1954-56).
  • [3] Landis, E.: A three-sphere theorem. Dokl. Akas. Nauk S.S.S.R., 148, 277-279 (1963).
  • [4] Landis, E.: Some problems of the qualitative theorey of second order elliptic equations (case of several variables). Uspekhi Mat. Nauk, 18, 3-62 (1963). Translated in Russian Math. Surveys, 18, 1-62 (1963).
  • [5] Miller, K.: Three circle theorems in parial differential equations and applications to improperly posed problems. Arch, for Rat. Mech. and anal., 16, 126-154 (1964).
  • [6] Protter, M., and H. Weingerger: Maximum Principles in Differential Equations. Prentice-Hall, Englewood Cliffs, N. J. (1967).
  • [7] Vyborny, R.: The Hadamard three-circles theorems for partial differential equations. Bull. Amer. Math. Soc, 80, 81-84 (1974).