Bulletin of the American Mathematical Society

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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.

Murray H. Protter and Hans F. Weinberger, Maximum principles in differential equations, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1967. MR 0219861

Herbert Amann, Fixed point equations and nonlinear eigenvalue problems in ordered Banach spaces, SIAM Rev. 18 (1976), no. 4, 620–709. MR 415432, DOI 10.1137/1018114

David Gilbarg and Neil S. Trudinger, Elliptic partial differential equations of second order, Grundlehren der Mathematischen Wissenschaften, Vol. 224, Springer-Verlag, Berlin-New York, 1977. MR 0473443

James Serrin, A symmetry problem in potential theory, Arch. Rational Mech. Anal. 43 (1971), 304–318. MR 333220, DOI 10.1007/BF00250468

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.

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, DOI 10.1007/BF00946979

L. E. Payne, Bounds for the maximum stress in the Saint Venant torsion problem, Indian J. Mech. Math. Special Issue Special Issue (1968/69), part I, 51–59. Special issue presented to Professor Bibhutibhusan Sen on the occasion of his seventieth birthday, Part I. MR 0351225

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, DOI 10.1016/0362-546X(79)90076-2

M. H. Protter and H. F. Weinberger, A maximum principle and gradient bounds for linear elliptic equations, Indiana Univ. Math. J. 23 (1973/74), 239–249. MR 324204, DOI 10.1512/iumj.1973.23.23020

1.

M. H. Protter and H. F. Weinberger, Maximum principles in differential equations, Prentice-Hall, Englewood Cliffs, N. J., 1967. MR 0219861

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