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Book Review
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Book Information
Author(s):
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:
- 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, Ni Wei-Ming and L. Nirenberg, Symmetry and related properties via the maximum principle, Comm. Math. Phys. 68 (1979), 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 problem, ZAMP 32 (1981), 683-694. MR 648766
- 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. 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), 193-211. MR 525971
- 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
Additional Information:
Reviewer(s):
Catherine
Bandle
Review Information:
Journal:
Bull. Amer. Math. Soc.
8
(1983),
343-345.
DOI:
10.1090/S0273-0979-1983-15112-1
PII:
S 0273-0979(1983)15112-1
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