A priori estimates and Blow-up behavior for solutions of $-Q_{N}u=V{e}^u$ in bounded domain in ${\mathbb{R}}^N$

Abstract

Let $Q_N$ be $N$-anisotropic Laplacian operator, which contains the ordinary Laplacian operator, $N$-Laplacian operator and anisotropic Laplacian operator. In this paper, we firstly obtain the properties for $Q_N$, 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 $-Q_{N}u=V{e}^u$ in bounded domain in ${\mathbb{R}}^N$, $N\ge 2$ are established. Finally, the behavior of sole blow-up point is further considered.

To appear in Sci China Math

References in corpus (1)

• Solutions for Toda systems on Riemann surfaces