We develop a lower and upper solution method for the Dirichlet problem associated with the prescribed mean curvature equation in Minkowski space {-div(∇u/√1-|∇u|2=f(x,u) in Ω u=0 on ∂Ω Here Ω is a bounded regular domain in ℝNand the function f satisfies the Carathéodory conditions. The obtained results display various peculiarities due to the special features of the involved differential operator.
Titolo: | On the lower and upper solution method for the prescribed mean curvature equation in Minkowski space |
Autori: | |
Data di pubblicazione: | 2013 |
Stato di pubblicazione: | Pubblicato |
Rivista: | |
Abstract: | We develop a lower and upper solution method for the Dirichlet problem associated with the prescribed mean curvature equation in Minkowski space {-div(∇u/√1-|∇u|2=f(x,u) in Ω u=0 on ∂Ω Here Ω is a bounded regular domain in ℝNand the function f satisfies the Carathéodory conditions. The obtained results display various peculiarities due to the special features of the involved differential operator. |
Handle: | http://hdl.handle.net/11368/2966173 |
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