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 [10.1007/s00526-009-0246-1].
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 [10.1007/s00526-009-0246-1]. | |
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 |
File in questo prodotto:
Non ci sono file associati a questo prodotto.
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.