Quasilinear elliptic systems involving the 1-Laplacian operator with subcritical and critical nonlinearities
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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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1-Laplacian operator, 35J62, 35J75, Critical nonlinearities, Elliptic systems, Space of functions of bounded variation
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Inglês
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Rendiconti del Circolo Matematico di Palermo, v. 73, n. 3, p. 1037-1058, 2024.
