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Book Review

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Book Information:

Author: René Sperb
Title: Maximum principles and their applications
Additional book information: Mathematics in Science and Engineering, vol. 157, Academic Press, New York, 1981, ix + 224 pp., $29.50.

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

  • 1. M. H. Protter and H. F. Weinberger, Maximum principles in differential equations, Prentice-Hall, Englewood Cliffs, N. J., 1967. MR 219861
  • 2. H. Amann, Fixed point equations and nonlinear eigenvalue problems in ordered Banach spaces, SIAM Rev. 18 (1976), 620-709. MR 415432
  • 3. D. Gilbarg and N. S. Trudinger, Elliptic partial differential equations of second order, Springer-Verlag, Berlin and New York, 1977. MR 473443
  • 4. J. Serrin, A symmetry problem in potential theory, Arch. Rat. Mech. Anal. 43 (1971), 304-318. MR 333220
  • 5. B. Gidas, Wei Ming Ni, and L. Nirenberg, Symmetry and related properties via the maximum principle, Comm. Math. Phys. 68 (1979), no. 3, 209–243. MR 544879
  • 6. N. J. Korevaar, Convex solutions to nonlinear elliptic and parabolic boundary value problems, Technical Report, University of Wisconsin-Madison, 1981.
  • 7. A. Acker, L. E. Payne, and G. Philippin, On the convexity of level lines of the fundamental mode in the clamped membrane problem, and the existence of convex solutions in a related free boundary proble, Z. Angew. Math. Phys. 32 (1981), no. 6, 683–694 (English, with German summary). MR 648766, https://doi.org/10.1007/BF00946979
  • 8. L. E. Payne, Bounds for the maximum stress in the Saint Venant torsion problem, Indian J. Mech. Math. special issue (1968), 51-59. MR 351225
  • 9. L. E. Payne and G. A. Philippin, Some maximum principles for nonlinear elliptic equations in divergence form with applications to capillary surfaces and to surfaces of constant mean curvature, Nonlinear Anal. 3 (1979), no. 2, 193–211. MR 525971, https://doi.org/10.1016/0362-546X(79)90076-2
  • 10. M. H. Protter and H. F. Weinberger, A maximum principle and gradient bounds for linear elliptic equations, Indiana Univ. Math. J. 23 (1973), 239-249. MR 324204

Review Information:

Reviewer: Catherine Bandle
Journal: Bull. Amer. Math. Soc. 8 (1983), 343-345
DOI: https://doi.org/10.1090/S0273-0979-1983-15112-1
American Mathematical Society