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On the lower and upper solution method for the prescribed mean curvature equation in Minkowski space
Chiara Corsato Franco Obersnel Pierpaolo Omari Sabrina Rivetti
We develop a lower and upper solution method for the Dirichlet problem associated with the prescribed mean curvature equation in Minkowski space \begin{equation*} \begin{cases} -{\rm div}\Big( \nabla u /\sqrt{1 - |\nabla u|^2}\Big)= f(x,u) & \hbox{ in } \Omega, \\ u=0& \hbox{ on } \partial \Omega. \end{cases} \end{equation*} Here $\Omega$ is a bounded regular domain in $\mathbb {R}^N$ and the function $f$ satisfies the Carathéodory conditions. The obtained results display various peculiarities due to the special features of the involved differential operator.
keywords: lower and upper solutions Mean curvature partial differential equation quasilinear Dirichlet condition existence elliptic Minkowski space multiplicity.

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