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