We show that the problem at critical growth, involving the $1$-Laplace operator and obtained by relaxation of $-\Delta_1 u=\lambda |u|^{-1}u+|u|^{1^*-2}\,u$, admits a nontrivial solution $u\in BV(\Omega)$ for any $\lambda\geq\lambda_1$. Nonstandard linking structures, for the associated functional, are recognized.
Degiovanni, M., & Magrone, P. (2009). Linking solutions for quasilinear equations at critical growth involving the $1$-Laplace. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 36, 591-609.
Titolo: | Linking solutions for quasilinear equations at critical growth involving the $1$-Laplace |
Autori: | |
Data di pubblicazione: | 2009 |
Rivista: | |
Citazione: | Degiovanni, M., & Magrone, P. (2009). Linking solutions for quasilinear equations at critical growth involving the $1$-Laplace. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 36, 591-609. |
Abstract: | We show that the problem at critical growth, involving the $1$-Laplace operator and obtained by relaxation of $-\Delta_1 u=\lambda |u|^{-1}u+|u|^{1^*-2}\,u$, admits a nontrivial solution $u\in BV(\Omega)$ for any $\lambda\geq\lambda_1$. Nonstandard linking structures, for the associated functional, are recognized. |
Handle: | http://hdl.handle.net/11590/142519 |
Appare nelle tipologie: | 1.1 Articolo in rivista |
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