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.
On the lower and upper solution method for the prescribed mean curvature equation in Minkowski space
Corsato C.;Obersnel F.;Omari P.
;Rivetti S.
2013-01-01
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.File in questo prodotto:
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