Research ArticleOpen AccessGoogle Scholar indexed
Extremum Principle for Very Weak Solutions of A-Harmonic Equation with Weight
- 1
- 2
- 3
Advances in Pure Mathematics·Volume 01 (2011)·Pages 235–237·Published 22 July 2011·DOI10.4236/apm.2011.14041
Copy link · social · email
Abstract
Extremum principle for very weak solutions of <i>A</i>-harmonic equation <i>div A</i>(<i>x</i>,▽<i>u</i>)=0 is obtained, where the operator <i>A</i>:Ω × <i>R<sup>n</sup></i>→<i>R<sup>n</sup></i>satisfies some coercivity and controllable growth conditions with Mucken-houpt weight.
Keywords<i>A</i>-Harmonic EquationMuckenhoupt WeightExtremum PrincipleHodge Decomposition
- 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
- J. Heinonen, T. Kil-pel?inen and O. Martio, “Nonlinear Potential Theory of De-generate Elliptic Equations,” Clarendon Press, Oxford, 1993.
- 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.
- D. Gilbarg and N. S. Trudinger, “Elliptic Partial Differ-ential Equations of Second Order,” Springer-Verlag, Berlin, 1983.
- 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