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EnglishWe investigate the existence of ground state solutions to the Dirichlet problem -div(|x|α∇u) = |u|2*α-2u in Ω, u = 0 on ∂Ω, where α ε (0,2), 2*α = 2n/n-2+α and Ω is a domain in R^n. In particular we prove that a non negative ground state solution exists when the domain Ω is a cone, including the case Ω = R^n. Moroever, we study the case of arbitrary domains, showing how the geometry of the domain near the origin and at infinity affects the existence or non existence of ground state solutions.
| Titolo: | On the existence of extremal functions for a weighted Sobolev embedding with critical exponent |
| Autori: | |
| Data di pubblicazione: | 1999 |
| Rivista: | |
| Abstract: | We investigate the existence of ground state solutions to the Dirichlet problem -div(|x|α∇u) = |u|2*α-2u in Ω, u = 0 on ∂Ω, where α ε (0,2), 2*α = 2n/n-2+α and Ω is a domain in R^n. In particular we prove that a non negative ground state solution exists when the domain Ω is a cone, including the case Ω = R^n. Moroever, we study the case of arbitrary domains, showing how the geometry of the domain near the origin and at infinity affects the existence or non existence of ground state solutions. |
| Handle: | http://hdl.handle.net/11390/680788 |
| Appare nelle tipologie: | 1.1 Articolo in rivista |
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http://hdl.handle.net/11390/680788
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