Quasilinear elliptic systems involving the 1-Laplacian operator with subcritical and critical nonlinearities

Abstract

In this paper, we study some systems of elliptic PDEs involving the 1-Laplacian operator. In the first one, we deal with the subcritical regime, while in the second, we study a system with nonlinearities with critical growth. The approach is based on an approximation argument, in which the solutions are obtained as the limit of related problems with the p-Laplacian operator. In order to overcome the lack of compactness in the critical case, a version of the Concentration of Compactness Principle of Lions is proved.