Spacelike graphs with prescribed mean curvature on exterior domains in the Minkowski spacetime

Abstract

We consider a Dirichlet problem for the mean curvature operator in the Minkowski spacetime, obtaining a necessary and sufficient condition for the existence of a spacelike solution, with prescribed mean curvature, which is the graph of a function defined on a domain equal to the complement in ${\mathbb{R}}^n$ of the union of a finite number of bounded Lipschitz domains. The mean curvature $H=H(x,t)$ is assumed to have absolute value controlled from above by a locally bounded, $L^p$-function, $p\in [1,2n/(n+2)]$, $n\ge 3$.

AMSLaTeX, 15 pages; v4: reference [37] updated

References in corpus (4)

• On the electrostatic Born-Infeld equation with extended charges
• Calabi-Bernstein results for maximal surfaces in Lorentzian product spaces
• On the regularity of the minimizer of the electrostatic Born-Infeld energy
• On the Born-Infeld equation for electrostatic fields with a superposition of point charges