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

Chiara Corsato; Franco Obersnel; Pierpaolo Omari; Sabrina Rivetti

doi:10.3934/proc.2013.2013.159

Article Contents

2013, Volume 2013: 159-169. Doi: 10.3934/proc.2013.2013.159 open access

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

1.
Dipartimento di Matematica e Geoscienze, Università degli Studi di Trieste, Via A. Valerio 12/1, 34127 Trieste

Received: August 31, 2012

Revised: February 28, 2013

Published: October 2013

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Abstract

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.

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Mathematics Subject Classification: Primary: 35J25; Secondary: 35J62, 35J75, 35J93, 35A01, 47H07.

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References

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