Quasilinear elliptic systems involving the 1-Laplacian operator with subcritical and critical nonlinearities. (English) Zbl 1540.35173
Summary: 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.
MSC:
| 35J57 | Boundary value problems for second-order elliptic systems |
| 35J62 | Quasilinear elliptic equations |
| 35A01 | Existence problems for PDEs: global existence, local existence, non-existence |
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