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MAXIMUM PRINCIPLES FOR SOME HIGHER-ORDER SEMILINEAR ELLIPTIC EQUATIONS

Published online by Cambridge University Press:  13 December 2010

A. MARENO
A. MARENO*
Affiliation:
Penn State University, Middletown, PA 17057, USA e-mail: aum24@psu.edu
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Abstract

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We deduce maximum principles for fourth-, sixth- and eighth-order elliptic equations by modifying an auxiliary function introduced by Payne (J. Analyse Math. 30 (1976), 421–433). Integral bounds on various gradients of the solutions of these equations are obtained.

Keywords

35B4535B50
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 53 , Issue 2 , May 2011 , pp. 313 - 320
Copyright
Copyright © Glasgow Mathematical Journal Trust 2010

References

REFERENCES

1.Danet, C.-P., Uniqueness Results for a class of higher-order boundary value problems, Glasgow Math. J. 48 (2006), 547–552.CrossRefGoogle Scholar
2.Dunninger, D. R. and Chow, S., A maximum principle for n-metaharmonic functions, Proc. Amer. Math. Soc. 43 (1974), 79–83.Google Scholar
3.Dunninger, D. R., Maximum principles for solutions of some fourth order elliptic equations, J. Math. Anal. Appl. 37 (1972), 655–658.CrossRefGoogle Scholar
4.Mareno, A., Maximum principles for a fourth order equation from thin plate theory, J. Math. Anal. Appl. 343 (2008), 932–937.CrossRefGoogle Scholar
5.Mareno, A., Integral bounds for von Kármán equations, Z.A.M.M. 90 (2010), 509–513.Google Scholar
6.Payne, L. E., Some remarks on maximum principles, J. Anal. Math. 30 (1976), 421–433.CrossRefGoogle Scholar
7.Schaefer, P. W., Uniqueness in some higher order elliptic boundary value problems, ZAMP 29 (1978), 693–697.Google Scholar
8.Schaefer, P. W., Solution, gradient, and laplacian bounds in some nonlinear fourth order elliptic equations, SIAM J. Math. Anal. 18 (1987), 430–434.CrossRefGoogle Scholar
9.Schaefer, P. W., Pointwise estimates in a class of fourth-order nonlinear elliptic equations, ZAMP 38 (1987), 477–479.Google Scholar
10.Sperb, R., Maximum principles and their applications, in Mathematics in Science and Engineering, vol. 157 (Academic Press, Inc., New York, 1981).Google Scholar
11.Tseng, S. and Lin, C.-S., On a subharmonic functional of some even order elliptic problems, J. Math. Anal. Appl. 207 (1997), 127–157.CrossRefGoogle Scholar
12.Zhang, H. and Zhang, W., Maximum principles and bounds in a class of fourth-order uniformly elliptic equations, J. Phys. A: Math. Gen. 35 (2002), 9245–9250.CrossRefGoogle Scholar