Some Weighted Inequalities on Polyharmonic Operators and Applications

Guo Dinghui

Volume 25 Issue 2

Feb. 1999

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Abstract

References

Journal of Beijing University of Aeronautics and Astronautics > 1999 > 25(2): 221-224.

Luo Mingqiang, Feng Haocheng, Liu Hu, et al. Rapid wing structure design and automated scheme adjustment for civil aircraft[J]. Journal of Beijing University of Aeronautics and Astronautics, 2009, 35(4): 468-471. (in Chinese)

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Guo Dinghui. Some Weighted Inequalities on Polyharmonic Operators and Applications[J]. Journal of Beijing University of Aeronautics and Astronautics, 1999, 25(2): 221-224. (in Chinese)

Citation:

Guo Dinghui. Some Weighted Inequalities on Polyharmonic Operators and Applications[J]. Journal of Beijing University of Aeronautics and Astronautics, 1999, 25(2): 221-224. (in Chinese)

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Some Weighted Inequalities on Polyharmonic Operators and Applications

Guo Dinghui

Beijing University of Aeronautics and Astronautics,Dept. of Applied Mathematics and Physics

Received Date: 24 Oct 1997
Publish Date: 28 Feb 1999

Abstract

Abstract

This work is devoted to weighted inequalities on polyharmonic operators and their applications to the critical exponent problems of semilinear polyharmonic operator with Dirichlet boundary value conditions. Some newer weighted inequalities on polyharmonic operator are obtained. By applying these new weighted inequalities to the critical exponent problems, it obtains a preferable necessary condition for nontrivial radial solutions of the critical exponent problems of semilinear polyharmonic operator with Dirichlet boundary conditions existing. This preferable necessary condition extends the scope in which the critical exponent problems has nontrivial radial solutions to two times of that in Bernis' paper.
- harmonic analysis,
- operators,
- critical exponent,
- boundary value problems

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References(1)

References

1. Bernis F, Grunau H C. Critical exponents and multiple critical dimensions for polyharmonic operators. J Diff Equations, 1995, 117(2):469~486 2. Brezis H, Nirenberg L. Positive solutions of nonlinear elliptic equations involving critical Sobolev exponents. Comm Pure Appl Math, 1983, 36(3):437~477 3. Edmunds D, Fortunato D, Jannelli E. Critical exponents, critical dimensions and the biharmonic operator. Arch Rational Mech Anal, 1990, 112(2):269~289 4. Noussair E S, Swanson C A, Yang J F. Critical semilinear biharmonic equations in R^N. Proc Royal Soc Edinburgh Sect, 1992(A),121(1):139~148 5. Pucci P, Serrin J. Critical exponents and critical dimensions for polyharmonic operators. J Math Pure Appl, 1990, 69:58~83

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Some Weighted Inequalities on Polyharmonic Operators and Applications