Extremum Principle for Very Weak Solutions of A-Harmonic Equation with Weight
Hong-Ya Gao, Chao Liu, Yu Zhang
.
DOI: 10.4236/apm.2011.14041   PDF    HTML     3,890 Downloads   7,799 Views   Citations

Abstract

Extremum principle for very weak solutions of A-harmonic equation div A(x,▽u)=0 is obtained, where the operator A:Ω × RnRnsatisfies some coercivity and controllable growth conditions with Mucken-houpt weight.

Share and Cite:

H. Gao, C. Liu and Y. Zhang, "Extremum Principle for Very Weak Solutions of A-Harmonic Equation with Weight," Advances in Pure Mathematics, Vol. 1 No. 4, 2011, pp. 235-237. doi: 10.4236/apm.2011.14041.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] T. Iwaniec and C. Sbordone, “Weak Minima of Varia- tional Integrals,” Journal für die Reine und Angewandte Mathematik, No. 454, 1994, pp. 143-162. doi:10.1515/crll.1994.454.143
[2] J. Heinonen, T. Kil-pel?inen and O. Martio, “Nonlinear Potential Theory of De-generate Elliptic Equations,” Clarendon Press, Oxford, 1993.
[3] H. Y. Gao, J. Li and Y. J. Deng, “Extremum principle for very weak solutions of A-harmonic equation,” Journal of Par-tial Differential Equations, Vol. 18, No. 3, 2005, pp. 235-240.
[4] D. Gilbarg and N. S. Trudinger, “Elliptic Partial Differ-ential Equations of Second Order,” Springer-Verlag, Berlin, 1983.
[5] H. Y. Jia and L. Y. Jiang, “On Non-Linear Elliptic Equation with Weight,” Nonlinear Analysis: Theory, Methods & Applications, 2005, Vol. 61, No. 3, 477-483

Copyright © 2024 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.