On the lower and upper solution method for the prescribed mean curvature equation in Minkowski space

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: 
CORSATO, CHIARA
OBERSNEL, Franco
OMARI, PIERPAOLO
RIVETTI, SABRINA
Data di pubblicazione: 2013
Stato di pubblicazione: Pubblicato
Rivista: 
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. SERIES S  
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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