摘要
Let Q_N be an N-anisotropic Laplacian operator, which contains the ordinary Laplacian operator,N-Laplacian operator and the anisotropic Laplacian operator. We firstly obtain the properties of Q_N, which contain the weak maximal principle, the comparison principle and the mean value property. Then a priori estimates and blow-up analysis for solutions of-Q_(N^u) = Ve^u in bounded domain in R^N, N≥2 are established.Finally, the blow-up behavior of the only singular point is also considered.
Let Q_N be an N-anisotropic Laplacian operator, which contains the ordinary Laplacian operator,N-Laplacian operator and the anisotropic Laplacian operator. We firstly obtain the properties of Q_N, which contain the weak maximal principle, the comparison principle and the mean value property. Then a priori estimates and blow-up analysis for solutions of-Q_（N^u） = Ve^u in bounded domain in R^N, N≥2 are established.Finally, the blow-up behavior of the only singular point is also considered.
基金
Excellent Young Talent Foundation of Anhui Province (Grant No. 2013SQRL080ZD)
