Some maximum principles for nonlinear elliptic boundary-value problems
Author:
Philip W. Schaefer
Journal:
Quart. Appl. Math. 35 (1978), 517-523
MSC:
Primary 35J25
DOI:
https://doi.org/10.1090/qam/479828
MathSciNet review:
479828
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Abstract: The Hopf maximum principles are utilized to obtain maximum principles for functions which are defined on solutions of nonlinear, second-order elliptic equations subject to Dirichlet, Robin, or mixed boundary conditions. The principles derived may be used to deduce bounds on important quantities in physical problems of interest.
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L. E. Payne and I. Stakgold, Nonlinear problems in nuclear reactor analysis, in Proc. Conference on Nonlinear Problems in Physical Sciences and Biology, Springer Lecture Notes in Math. No. 322, 298–307 (1972)
L. E. Payne, R. P. Sperb, and I. Stakgold, On Hopf type maximum principles for convex domains (to appear)
- L. E. Payne and G. A. Philippin, Some applications of the maximum principle in the problem of torsional creep, SIAM J. Appl. Math. 33 (1977), no. 3, 446–455. MR 455738, DOI https://doi.org/10.1137/0133028
- Murray H. Protter and Hans F. Weinberger, Maximum principles in differential equations, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1967. MR 0219861
- 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 https://doi.org/10.1512/iumj.1973.23.23020
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- P. W. Schaefer and R. P. Sperb, Maximum principles and bounds in some inhomogeneous elliptic boundary value problems, SIAM J. Math. Anal. 8 (1977), no. 5, 871–878. MR 492825, DOI https://doi.org/10.1137/0508066
V. Komkov, Certain estimates for solutions of nonlinear elliptic differential equations applicable to the theory of thin plates, SIAM J. Appl. Math 28, 24–34 (1975)
L. E. Payne, Bounds for the maximum stress in the Saint Venant torsion problem, Indian J. Mech. and Math. Special Issue, 51–59 (1968)
L. E. Payne and I. Stakgold, On the mean value of the fundamental mode in the fixed membrane problem, Appl. Anal. 3, 295–306 (1973)
L. E. Payne and I. Stakgold, Nonlinear problems in nuclear reactor analysis, in Proc. Conference on Nonlinear Problems in Physical Sciences and Biology, Springer Lecture Notes in Math. No. 322, 298–307 (1972)
L. E. Payne, R. P. Sperb, and I. Stakgold, On Hopf type maximum principles for convex domains (to appear)
L. E. Payne and G. A. Philippin, Some applications of the maximum principle in the problem of torsional creep (to appear)
M. H. Protter and H. F. Weinberger, Maximum principles in differential equations, Prentice-Hall, Inc. (1967)
M. H. Protter and H. F. Weinberger, A maximum principle and gradient bounds for linear elliptic equations, Indiana U. Math. J. 23, 239–249 (1973)
P. W. Schaefer and R. P. Sperb, Maximum principles for some functionals associated with the solution of elliptic boundary value problems, Arch. Rational Mech. Anal. 61, 65–76 (1976)
P. W. Schaefer and R. P. Sperb, Maximum principles and bounds in some inhomogeneous elliptic boundary value problems, SIAM J. Math. Anal. 8 (1977)
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Article copyright:
© Copyright 1978
American Mathematical Society
