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.
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Acknowledgements
Marcos T.O. Pimenta is partially supported by FAPESP 2021/04158-4, CNPq 304765/2021-0 and FAPDF, Brazil. Yino Beto Cueva Carranza is supported by CAPES/Brazil 001.
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Carranza, Y.B.C., Pimenta, M.T.O. Quasilinear elliptic systems involving the 1-Laplacian operator with subcritical and critical nonlinearities. Rend. Circ. Mat. Palermo, II. Ser 73, 1037–1058 (2024). https://doi.org/10.1007/s12215-023-00969-2
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DOI: https://doi.org/10.1007/s12215-023-00969-2